I'm not sure if this is the right circle to post, but I feel like it's the most relevant.
for me personally, I don't think they should be included with LGB for the following reasons -
asexuals aren't killed, ostracised, bullied etc just for being asexual. asexual women may be pressured into getting married to men, but that's just misogyny. lesbians go through the same thing, and so do basically single women of any age and orientation. ace men may be made fun of for being virgins, but that's just toxic masculinity. any virgin guy would experience that.
asexual can sometimes be not innate, as in, a trauma response. sexual trauma from childhood or any time of your life really, can cause you to be asexual, especially sex-repulsed. no amount of trauma or life experience can turn a straight person gay. that's a very important distinction, and I don't doubt that it might lead to conversion therapy narratives against gays and lesbians.
sidenote: this is personal (and maybe only happens online), but I've seen so much ace homophobia. I'm not sure if y'all noticed, but yeah. I was in a fb group that archived/pointed out examples of asexuals being homophobic, and there were asexuals in that group too. they (homophobic aces) made fun of gay men for being infected with HIV, by saying stuff like "haha, I'll never have HIV! I don't fling myself at random people" during a conversation about that epidemic, in regards to LGB issues. it was a tumblr post, I'm not sure how to find it, but the hyperlink is to a tumblr blog that points out ace homophobia. I've never used tumblr, and maybe this is just a very online phenomenon.