I'm not sure I can beat the entertaining tone in u/Turtledonuts' post on the McRoman, but I'll do what I can to help you imagine the Roman SweetGreen (viridis dulcis?).

Our best source for food of the later Roman Empire is the de re coquinaria/On Cooking, commonly attributed to a man named Apicius, who may have lived in the 1st c. AD. His work is a remarkable resource in that it is, essentially, a cookbook - something the Romans didn't seem to have need nor want of, as this is basically the only one known, though there were a number of Greek works on cooking and food from earlier periods (Archestratus' work, ca. 350 BC, was on how to find and cook good fish (now only known in fragments); Athenaeus, ca. 200 AD, who quoted other lost Greek works on food in his Deiphnosophists/Table Talk, and Chrysippus of Tyana and Paxamus, whose works are both lost), and Cato the Elder wrote a bit about food in his de agricultura/On Farming, including a relevant section here: in praise of cabbage (which has some recipes but is more about how to use it for health - including, if a person eats enough cabbage, their "urine will be good for everything," (156, 1) and you should save it to "bathe the person in it; he will be healed quickly" (157, 10)

Let's ignore Cato from this point on (ergh); you asked about the later Empire, and he was not only much earlier, but a well-known miser, and later sources give us much more appetizing food possibilities!

Apicius has a few recipes for salad, including what we would easily recognize as a dish based off of green, leafy vegetables, dressed in some liquid to enhance the flavor (yes, the Romans used salad dressing - well done, though for noting that salad-recipe.net isn't a reliable historical source!). Apicius has an entire book on vegetables, and if you look for leafy greens, you'll see that lettuce, endive, cabbage, field herbs, and other vegetables that have edible green tops (turnips, beets, etc) are all listed. A key factor in being a good cook is adapting to what is available, I'd argue, so any cook in the Roman world worth their salt (heh) would have been able to work with what they could get, what was in season, what their budget could afford, etc to make a salad with. Apicius also gives us a recipe that looks a lot like the basis for any modern salad:

Lettuce Salad (agrestes lactucae): dress it with vinegar dressing and a little brine stock, which helps digestion and is taken to counteract inflation.

or: Field Herbs (herbae rusticae): Field and forest herbs are prepared either raw or with stock (brine?), oil, and vinegar as a salad or as a cooked dish by adding pepper, cumin, and mastich berries.

(the 'as a salad' part may be transcribed from the surviving manuscripts as 'a manu' - "eaten by hand" - so this could be an interpretation by the editor of the only English text I was able to find (I don't have the Latin accessible to me, unfortunately))

This section also has a few different types of things that might be used as dressing: for example, "2 ounces of ginger, 1 ounce of green rue, 1 ounce of meaty dates, 12 scruples of ground pepper, 1 ounce of good honey, and 8 ounces of either Aethiopian or Syrian cumin. Make an infusion of this in vinegar, the cumin crushed, and strain. Of this liquor use a small spoonful, mix it with stock and a little vinegar." (III.111); all translations taken from Vehling, 1936, as noted on Lacus Curtius)

Another option is a cucumber dressing: "cucumber, pepper, pennyroyal, honey or raisin wine, fish sauce, vinegar. Sometimes also asafoetida." (Dalby and Grainger, p. 118; Apicius 3.6.3)

Apicius has a few other options, though; just as we see salad as something that can be based on grains or even meat, depending on preparation, so did he:

Chicken Salad (sala cattabia): Put in a mortar celery seed, dried pennyroyal, dried mint, ginger, coriander leaf, seeded raisins, honey, vinegar, oil, and wine. Crush. Put in a pan bits of Picentine bread, layered with chicken meat, kid's sweetbreads, Vestine cheese, pine kernels, cucumbers, dried onions chopped fine. Pour the liquid over. At the last moment, scatter snow on top and serve." (Dalby and Grainger, 103) That last bit is interesting - again, wish I had access to the Latin - because Vehling gives the translation as "cover completely with a lukewarm, congealing broth, place on ice and when congealed umould and serve up." Either way, it seems we have either a tossed dish including numerous vegetables, meat and organ meat (which the Romans prized highly and priced highly as well), and a dressing, or a moulded salad which reminds me of the aspics popular around the 1950s/60s.

If you're curious what kinds of things the Romans would have had access to: since you specifically mention the later Empire, the answer is pretty much anything, if they could pay for it. At the height of the Empire, food came into Rome and other cosmopolitan cities from essentially all over the known world, and the upper-class were rabid consumers of exotic ingredients - so much so that some plants were possibly harvested into extinction, such as silphium (aka laser), an herb from Cyrenaica (Libya) used for food, perfume, as an aphrodisiac, etc which had disappeared almost entirely by the time of Nero. We know from texts like Petronius' Satyricon, and specifically the Dinner with Trimalchio chapter that indicate Roman cooks were wildly inventive and liked to show off not only their skill with ingredients, but the exotic and expensive materials available to them; so the sky was probably the limit with food, at that time, with the ingredients available then. To get a sense of what was available in Rome, and the prices of such goods, have a look at the Emperor Diocletian's Price Edict (301 AD). ( u/Skipp_To_My_Lou rightly points out that I wasn't clear that a lot of things we associate with salads today - like tomatoes! - are native to the Americas and thus weren't available for the Romans.)

Another thing to add, though, is that there likely weren't a lot of salads - raw, vegetable salads, that is - consumed at that time, as anything uncooked was more likely to carry pathogens than something exposed to heat. Apicius notes a few times that lettuce may harm you (that first dressing recipe I noted above is called ne lactucae laedant ('that the lettuce will not harm,' or "a harmless salad" as written by Vehling), and is introduced with "In order that the lettuce may not hurt you, take with it or after it, the following preparation..." This is likely to be more about the possibility that eating raw vegetables could lead to disease or diarrhea - we know today too well about e.coli outbreaks on Romaine, etc! - than an actual fear of lettuce itself.

If you're interested in cooking up a few Roman recipes, some authors - Sally Grainger, especially - have translated Apicius' sparse notes into modern equivalents; I'll list her work in the sources, below.

Sources (secondary):

Dalby, Andrew, and Sally Grainger, 1996. The Classical Cookbook. (J. Paul Getty Museum)

Grainger, Sally, 2006. Cooking Apicius: Roman Recipes for Today. (Prospect Books)

Vehling, Joseph Dommers, 1936. Cookery and Dining in Imperial Rome: A Critical Review and Translation of Apicius' De Re Coquinaria. (Walter Hill)

Sources (primary):

Apicius, de re coquinaria

Cato, de agricultura

Diocletian, edictum de pretiis rerum venalium

While you wait, please enjoy this all-time great answer by u/Turtledonuts to "Would it have been possible for a roman citizen around 1 A.D. to obtain everything needed to make a Cheeseburger, assuming they had the knowledge of how to make one?"

Best way to get at this is the only extant Roman cookbook- De Re Coquinaria by Apicius (compiled in the fifth century, it's unclear if it is based on something since lost from the first century AD).

In short- We'd recognize salads from ancient Rome. There are some ingredients they used that have fallen out of favor (mostly herbs like rue, pennyroyal, and lovage) and other ingredients we use now that they didn't have access to yet (like tomatoes), but in general the concept of that dish existed and hasn't changed too much over the millenia. Btw- I'm defining salads here as a cold dish of vegetables with some sort of dressing. I know there are many other things that get called salads but we've got to have something to focus on.

Some recipes from the text:

Herbs with stock, oil and vinegar (served cold, or cooked adding pepper, cumin, and mastich berries). The stock feels like an odd addition, but otherwise this just a basic green salad. No tomatoes to add to this simple salad because those are a New World food.

They did have cucumbers though- there's another recipe for cucumbers with pennyroyal, pepper, honey or condensed must, broth and vinegar. There's also a recipe with the same dressing, but replacing the cucumber with melon.

Lettuce, dressed with vinegar and some brine stock (unclear if the other recipes use brine stock or some other kind, but it definitely makes sense as a way to add salt, the etymologic base for 'salad.' This simple lettuce salad comes with an optional and more complex dressing (ginger, rue, dates, pepper, honey, cumin, vinegar). Honestly sounds pretty good.

Cardoons with briny broth, oil, and chopped hard boiled eggs. (I'm not a fan of hard boiled eggs on anything but they've been on salads for a long time).

Rue, mint, coriander, fennel greens, pepper, lovage, brine, oil. (mixed herb salad- no vinegar though, guess the author figures the greens are a strong enough flavor).

Would they have used meat? There are recipes for sauces for meats that are very similar to the above dressings. For example, there is a recipe for boiled chicken served with a cold dressing of dill seed, laser root, mint, vinegar, fig wine, broth, mustard, oil, and must. Not exactly a modern chicken salad but certainly something we might call a salad with meat.

There's also a recipe for boiled spiny lobster, dressed with pepper, lovage, celery seed, vinegar, broth, and boiled egg yolks. Seafood salad, more or less.