This is actually a great question that I can't fully answer but I can provide some historical context about shoelaces in Europe (or at least, France). Basically, lacing shoes began as a sort of poor-man's way of dealing with shoes that required buckles, which were more expensive than the shoe itself. Thus the idea of a "laced" shoe wasn't a shoe with laces, it was a shoe without buckles, a sign of impropriety.

The interesting thing about fasteners for clothing is first, they're made of something different than the rest of the article of clothing, for example metal, and second, they can be re-used on different articles of clothing. Unlike a shirt or a tunic or leggings, metal buckles and buttons don't wear out very easily, and thus they were valuable possessions that circulated throughout the population. Essentially think of buttons and buckles like how folks think of cufflinks today--they have a value separate from the cuffs they are being used to link.

As with anything that's wearable and shiny, it was adopted as a means for the wealthy (nobles, and later the bourgeoisie) to show off their status and wealth. Sartorial splendor was fundamental to the social order, both reinforcing and constituting the legitimacy of the nobility. Buttons and buckles were just one part of the vocabulary of superiority.

For the poorer folks, to have a metal button was a prized possession, and one of the most remarkable and often overlooked changes that occurred in Early Modern Europe as a result of increased state attentiveness to producing standardized military uniforms, especially in the late 18th century with France and the levée en masse, was the amount of second-hand clothing, particularly buttons, that spread throughout the population of Europe.

What if you can't afford a buckle, but you can afford a pair of shoes? This is where lace comes in. Indeed, because buckles and buttons were associated with the nobility, and then the wealthy bourgeoisie, and then the idle aristocracy, they were called into question by Enlightenment criticism. During the French Revolution, Jean-Paul Marat famously refused to abide by strictures of bourgeois sociability, and walked around in a disheveled state consisting of, among other disheveled traits, laces holding his shoes closed. Of course, not everyone was like Marat, but he was making a statement about buckles being frivolous and (perhaps inadvertently) saw shoelaces as the wave of the future. If only he hadn't been murdered in his bathtub, he may have changed the history of shoes!

This is where my period ends, so I can't actually answer your question, but hopefully you found this little bit interesting and I expect someone who knows more about 19th/20th century industrialization can answer the question of shoelaces.

but as far as European history goes I'm aware of Roman sandals, strap-and-buckle type shoes and slippers of the Middle Ages, and then suddenly shoes you lace up and tie sometime in the 19th century

Actually Roman footwear and especially Greek footwear was almost entirely laced. The Romans knew about buckles, and the stereotypical "Greek" sandal with its elaborate criss-crossing ribbon-like straps is a Roman style of footwear, not Greek. But even among the Romans buckles are not nearly so common as modern fashion designers and Hollywood would have you believe. And outside of sandals (and even including them), which were only rarely worn out of doors at Rome, laces were the rule. The calceus, the leather ankle boot that Roman citizens wore in public (to quote an older answer of mine: "a Roman senator clad in sandals outdoors was the object of derision"), was quite conspicuously laced and tied up the ankle