Have we ever seen an African-American version of this character in the comics?

As far as I know, Luthor has never been depicted as a black man in the comics.

I checked his disambiguation page at dc.fandom.com to make sure, and couldn't see a black version of Luthor from the comics there.

In general, the changing of a character's race (even in alternate universes) seems to be less of a thing in superhero comics than it is in other media.

Luthor was, however, ostensibly depicted as black in the Harley Quinn TV series.

Aside from how he was drawn and coloured, he was also voiced by a black actor, Giancarlo Esposito, who appears to confirm that his version of Luthor was indeed black in the video interview below:

This is also confirmed by the following statement from the Harley Quinn showrunners (Justin Halpern and Patrick Schumacker), made in an email sent to Collider:

But Halpern and Schumacker say that Harley Quinn "does conceive of Lex Luthor to be a person of color. We're not sure if we are the first to make Lex a POC, but DC was supportive when we said we wanted to go in that direction, which was cool.”