This is a great question, and one that needs a lot more study. Disability studies in Classics is a growing field, but unfortunately that means it's also one which has been largely neglected until very recently. A 2013 edited volume from a major Classical publisher claimed to be 'the first volume ever to systematically study the subject of disabilities in the Roman world' - which isn't quite accurate, but gives you an idea of the state of the field.^(1)

In part, the lack of scholarly attention exists because scholars have assumed that disabled people didn't have much of a life expectancy in the Ancient World - and while that's a huge oversimplification, it's worth bearing in mind that the sort of injuries that would leave you with a lifelong disability were much less survivable in the Roman world than they would be today. As I've written in another answer, the Romans knew that even the best surgery carried a good chance of killing the patient rather than curing them, and the odds of surviving something traumatic like an amputation would have been less than even.

Disability, however, doesn't have to equate to injury, though we do have plenty of accounts of men disabled in war. In one part of his account of the Civil War (2.53), for instance, Julius Caesar recounts a particularly ferocious day's fighting in which 'not a single one of the men was not wounded, and four centurions out of one cohort were blinded.' We can't read too much into this, but I think it's interesting that he establishes three categories of 'dead', 'wounded' and 'notably wounded', and then fills the latter only with men who lost their sight - which may suggest that there weren't many others left severely disabled, because those men hadn't survived. With that said, we do find prosthetics as archaeological remains (see the Capua Leg, for instance, buried with its owner around 300 BC), and accounts of people using them in literary sources - most famously, of the general Marcus Sergius Silus, who lost his right hand during the Second Punic War and had it replaced with an iron one.^(2) Robert Garland even goes as far as to argue that dangerous work, unsanitary conditions, malnutrition, disease, illness, and aging would have made some level of disability 'so common as to be the norm.'

In one letter, written by Pliny the Younger in the early 2nd century AD, there's an account of a senator called Gnaeus Domitius Tullus. As Pliny tells it, Tullus became almost totally paralysed sometime in middle or old age, and his account reveals a lot about how someone like him could adapt to life as well as the attitudes of Roman society towards him:

It was thought most unsuitable that a woman of [his wife's] high birth and blameless character, who was no longer young, had borne children in the past and had long been widowed, should marry a wealthy old man and a hopeless invalid, whom even a wife who had known him when young and healthy might have found an object of disgust. Crippled and deformed in every limb, he could only enjoy his vast wealth by contemplating it and could not even turn in bed without assistance. He also had to have his teeth cleaned and brushed for him – a squalid and pitiful detail – and when complaining about the humiliations of his infirmity was often heard to say that every day he licked the fingers of his slaves. Yet he went on living, and kept his will to live, helped chiefly by his wife, whose devoted care turned the former criticism of her marriage into a tribute of admiration.^(3)

On one level, we have the support systems familiar throughout history - the family, here in particular his wife. On the other, we can see how Tullus' 'vast wealth' was helpful in being able to pay for slaves and insulate him from the need to work to survive. Jane Draycott has also pointed out that the two stories of Silus and Tullus show different sides of the Roman attitude to disability - the elder Pliny used Silus' disability to show his masculine virtue and defiance of it, while the younger presented Tullus' condition as humiliating and as something for able-bodied people to look at and count their blessings.^(4) Both stories, in other words, engage with disability only from the perspective and in the interests of able-bodied people: they aren't authentic disabled perspectives and aren't particularly concerned with recovering the disabled person's experience of life.

One issue that comes up regularly in this sort of study is that of infanticide - and this is very much a moving target in the last few years and even months, so I will try to prevaricate on that except to point to the work of scholars like Debby Sneed, who has material in press suggesting that much of what we 'know' about infanticide (in particular, the 'fact' that it was fairly common to expose or outright kill disabled newborns in the Greek world) rests on shaky evidence and should be taken with a great deal of caution. There's an account in the Late Antique biography of St. Martin, written by Gregory of Tours, that has some bearing on the matter:

At Bourges a woman gave birth to a son, whose knees were bent up to his stomach; his heels were fastened to his legs, his hands hugged his chest, and his eyes were closed. He looked more like a monster than a human being. Many looked at him with laughter and the poor mother was criticised because such a monster had come out of her. In tears, she confessed that she had conceived him on a Sunday night. Since she did not dare to kill him, she raised him as a healthy child, as mothers usually do. When he got older, she handed him over to beggars, who placed him on a cart and dragged him around, displaying him to the people, who gave lots of money to watch the prodigy. This went on for a long time, and when he reached the age of ten years, he arrived at Saint Martin’s feast. He was left outdoors and lay in misery before the saint’s tomb.

It's not sensible to try to reconstruct a 'diagnosis' from this story (as with all ancient 'historical' texts, it's fundamentally a work of literature and shouldn't necessarily be taken literally), but it does suggest that killing a disabled child was common or condoned enough that the mother would have to explain why she didn't do it. However, this is also far from the only story of a severely disabled person being displayed as a kind of 'freakshow' to beg for money, or even sold as a slave and curiosity. Christian Laes draws attention to the phrase 'as mothers usually do', suggesting that this may point to a social stereotype that fathers would normally kill a child in this position, but that mothers would be seen as more likely to raise the child.^(5) So we really have light on two points of ancient disability here - firstly, the possibility that a disabled child would simply not be allowed to live very long, and secondly, the sort of life that might await them if they did.

This is pretty much as far as we're able to go - if you flick through any of the volumes mentioned below, you'll find firstly that they overwhelmingly concentrate on disabilities 'above the neck' (that is, blindness, deafness, speech impairment and learning difficulties), and secondly that they overwhelmingly focus on (able-bodied peoples') attitudes towards disability and how disabled people were thought of, rather than being able to reconstruct life from their point of view. This is, unfortunately, a reflection of our sources - as ancient historians, we are always working with a highly partial set of evidence, which skews overwhelmingly towards the voices of mostly-able-bodied, elite men. Going any further is really a matter of inference - and here I'd point you towards a recent article by Debby Sneed, who has noted that Greek temples, particularly healing sanctuaries, often included ramps as part of their architecture, which seems to suggest that they were thinking about accessibility by people of limited mobility.^(6) You'll notice that I haven't even tried to limit the answer to the Republican period, because the quantity of evidence there would drop from 'too little' to 'barely any'. Ultimately, it becomes extremely difficult to write a history of ancient disability that isn't fundamentally a history of ancient attitudes to it.