If I understand the progression they went through designing Tomb Raider's protagonist, Core Design started off with "Let's make a game called Tomb Raider, it's about exploring ancient ruins and collecting relics and artifacts." So they designed the player character as a man with a whip and a hat and then said "Blimey that's Indiana Jones, we can't do that or Spielberg will sue our bollocks off." And someone said "Hey there's an idea, let's make the character female."

So they came up with a feisty Latin American woman named Laura Cruz. But depending on whose telling the story, either they couldn't find a voice actress that could do a reasonable Latina accent in Derby England, or the publisher wanted a "more UK friendly" read whiter name, so they changed it to Laura Croft. But for some crumpet-related reason they thought Americans wouldn't be able to pronounce "Laura" thinking it an uncommon name over here (it isn't, we've got lots of Lauras), so they changed it to "Lara" which is genuinely unknown over here.

So then a bunch of things happened at once:

People don't actually read every single letter in a word, whcih is why yuo cna raed tihs jsut fnie, so the word "Lara" was perceived as the word "Laura" subconsciously.
People hearing the name "Lara" spoken aloud aren't familiar with it, found the closest to it in their memory, which is Laura, and went with that.
"Lara" pronounced somewhere between "LAAH-ruh" and "LAY-rah" is unwieldy to say in many American accents so many people spoke it aloud as "LAHR-uh" or "LORE-uh" which are very close or identical to how we pronounce "Laura," further compounding the above point.
Apple and Google don't know what the fuck they're on about either and their phone's autocorrect feature changes it to Laura without them noticing.