I speak like two words of Spanish, so my information on the usage of apostrophe in regards to elision in Spanish could very well be mistaken, I just like learning about languages. However I'm not referring to the tilde above a letter.
Did some more investigating and it does appear to be antiquated now, so thanks! Always happy to learn something new. When reading back up on elision I had seen that there are use cases, for example, wherein "para" would be reduced to "pa" and is often written as Pa' to signal the deletion of "ra".
ElisionLooked more and found a reddit thread talking about elision where someone responded "Nowadays you only see it to represent the pronunciation of certain dialects: "p'allá", "pa' ti", etc."
Feel free to let me know if that's wrong as well though.
Still to my original point though, whether actively used or not there are potentially valid reasons to include an apostrophe in a name, in the specific case of Lae'zel to keep people calling her 'Lie-zel" instead of "Liez-ell", a small change to be sure but at least adds some consistency to how people say her name. Aesthetically it doesn't bother me either, though that's not really that important.