Well, it's not the same thing, but you could always promote your work via LGBTQ+ WebSerials, they only do novels.
I'm sure there are award things for novels too out there, but you're going to find them yourself. I only have comic resources because I'm working on a webcomic, novels aren't necessarily relevant to me. Twitter is where I found most of my stuff, you might be able to find ways to get more eyes on your work there. Search up "LGBT fiction" or other similar tags, you're bound to find reviewers, "Share your work" threads and maybe even relevant events. Professional novelists also share resources sometimes, scroll through the profiles of some of your favorite LGBT+ writers, you may find something useful.
Twitter is a cesspool, but you'll find some good shit on there if you know where to look.