From what I can tell, most Classical authors use Lakedaimon where most modern writers use Sparta; modern translators often convert the former to the latter when rendering ancient texts, i.e.

ὦ ξεῖν', ἀγγέλλειν Λακεδαιμονίοις ὅτι τῇδε κείμεθα τοῖς κείνων ῥήμασι πειθόμενοι.

Go, tell the Spartans, stranger passing by/That here, obedient to their laws, we lie.

What gives? Did everyone just decide to switch to the easier spelling at some point?