Lara Croft is an Icon in the West and that's about it. Japan sees her as more of a fashion model then an adventurer, likely due to seeing her in ads more then playing the games.
She also had a fall from grace like Crash and Spyro and only recently is coming back into the spotlight..but not to anywhere near the degree of popularity she once had. Beyond that, reboot Lara isn't the iconic one, the 90s/00s one is.
However, I mostly meant in regards to fan demand. Fact is there are very few people that actually want Lara Croft in Super Smash Bros. Square Enix has a ton of characters with more fan demand then Lara has, and more popularity if you consider the massive popularity of Dragon Quest in Japan.
Not helping her case is that Sakurai likes to converse with the character's creator or handler, which is why no Western IPs are in as playable characters, and the team behind Lara's games are Western, even if the parent company is Japanese.
Lara may be a popular character and a past Icon, but I do not believe most people would love her inclusion over so many other wanted characters even from just SE alone.