Are they pronounced the same anywhere?
Not to my knowledge. The closest thing I can think of is that in some parts of Australia and New Zealand they merge "celery" and "salary", but that has to do with the /l/.
They are not pronounced the same here in southeastern Wisconsin, but "lattice" is often pronounced similar to (but generally not quite identical to) how "lettuce" is pronounced in other dialects. "Lattice" is generally [ˈɰɛ̯æɾ̥ɨs]/[ˈɰɛ̯æːɨ̯s]/[ˈɰɛ̞ɾ̥ɨs]/[ˈɰɛ̞ːɨ̯s] and "lettuce" is generally pronounced [ˈɰɜ̟ɾ̥ɨs]/[ˈɰɜ̟ːɨ̯s] here. The vowel [ɛ̞] in particular that often shows up in less stressed or careful speech seems to often be perceived by speakers of other dialects outside the Inland North region as being historical /ɛ/, even though historical /ɛ/ here is actually normally [ɜ̟].