Does lab-grown/cultured meat count as vegetarian because no animal suffering was involved and it's more like an animal product like milk/cheese/eggs, or not count because it's meat?

I'd put the chance at >5% that we get lab grown meat that is cheaper and tastier than factory farmed meat by 2035.

Let's take the Stonewall riots (Jun 1969) as a rough estimate of when homosexuality "entered the discourse" at a societal level. After that, it took ~40y for a majority of Americans to accept same-sex (civil) marriage [1]. (Forty years is the time it takes for ~half the population to die, so some may conjecture you get a change in societal views once holders of the old view die off.)

I'd say vegetarianism has already "entered the discourse" in the US, but it happened for sure less than 20y ago, maybe less than 15y ago. More importantly, "accept same-sex marriage" is a very low-effort action to take, compared to being vegetarian. So I'd say the odds here are well under 1% (unfortunately).

[1] https://en.wikipedia.org/wiki/Public_opinion_of_same-sex_marriage_in_the_United_States#Overview