A Blc. is a Cattleya Alliance hybird consisting of Brassovola, Laelia and Cattleya
Because of name changes in taxomony -
Your Blc (Brassolaeliacattleya) is now a Thwaitesara (Thw.) which is an hybrid comprising of Cattleya, Guarianthe, Rhyncholaelia and Sophronitis.
So leave it as Blc. but note the Thw. for future reference.
It will do great if you had a southern exposure as Catts love strong bright light. I can be slowly introduced into sunlight as sudden light intensity can burn it.
I'm not sure about supplemental lighting but I am sure others will advise you on that