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In English, prepositions have something in common with most grammatical morphemes: they're a closed class. However, some phrasal prepositions in English contain lexical morphemes: "on top of," "on the bottom of," "on the side of" ... and more.
I admit, I don't know whether there are languages whose adpositions constitute an open class, which is why I'm asking the question here rather than on the English Stack Exchange.
As usual, it depends on what you think "functional" and "lexical" mean. They certainly are a closed class (understood to mean new forms aren't as readily innovated as the typical open classes of nouns, verbs, adjectives). If that's what you mean by "functional" then they're certainly functional, at least in the languages I'm aware of.
There are other properties that make them look "lexical," e.g. some of them bear default stress, but that's probably a historical accident related to the fact that a number of English prepositions are transparently derived from nouns.
Which leads me to something that might interest you. The term "preposition" (or "adposition") applies to several different kinds of things. For instance the "phrasal preposition" on top of contains a kind of pseudo-noun top, which is definitely not a noun (try checking it for some properties of nouns, it doesn't have them). This kind of thing appears all over the place, many different languages have something similar. You can find this discussed in these papers (1, 2) by Peter Svenonius. He mentions a few other languages. He also says something about functional/lexical on p13 in the second paper.
