Welcome Fleur!
I do grow a bunch of rupicolous Laelias. Now I grow them here in NJ in maximum sun, in Winter in the greenhouse right under the glass ceiling, (in Summer outside unprotected/in full sun.) Since they dry up very quickly, I have some potted in small stones, some mounted, I water daily with rain water. Inside they get plenty ventilation from a nearby fan.
Some of mine bloom reasonably easy for me, some not or never. L. liliputana sat there for years, never bloomed and managed to die last Summer.
Laelia mixta blooms more reliable. It is in bloom now.
I should add, yes, getting new growth on some of those can be a bit of a challenge. Sometimes at the end of the Summer outside, you have beautiful new growths, only to see them turning black and you lose half of the plant or the whole thing just peters out.