Sorry if I’m wrong, but doesn’t lxappearance only set the GTK-2 theme? You set the GTK3 theme via dconf or set the GTK3/4 theme using the GTK_THEME env var. There are hardly any apps that use GTK-2 anymore; only one I can think of off the top of my head is PCManFM.
Btw, if you want rounded corners, blur, and window shadows in sway, consider checking this out: https://github.com/WillPower3309/swayfx It’s availible in the AUR, too.