i've yet to formally mention/elaborate upon the luteces gender and pronouns.
robert is comfortable with he/they/she pronouns.
before jumping into rosalind's universe, robert only used he/him. once entering rosalind's world, and obtaining all of rosalind's memories (as well as retaining his own), robert became innately but not overtly comfortable with she/her pronouns. however, using she/her pronouns is not something he would ask people to do. if someone accidentally referred to him as such, it simply wouldn't feel wrong or foreign. it's more nuanced than "he has rosalind's memories and rosalind is a woman so he has the memories of a woman and feels like a woman because of that". yes, that's a large part of it--the blurring of selves/identities. but it's also this: having been shown/felt/opened to a feminine existence (via rosalind's memories), he was able to reflect and explore those aspects dormant within himself. that and he is no longer the robert he was before entering rosalind's world. he is inextricably changed and different and other.
similarly, once in rosalind's world, and living as an inseparable unit with her, they/them felt like a natural and frequent pronoun. as they are always together, people often refer to them as one: them. and as "twins" (AND as beings that exist beyond the rules of physics (alive and dead all at once)), they feel a certain fond affinity towards the paradoxical/both-are-true-at-once singular/plural they/them pronouns. what's more, with the blurring of his identity with hers (man and woman), they/them feels like a neutral compromise of the two.
rosalind is comfortable with she/they pronouns.
she/her for obvious reasons. they/them for the same reasons as robert, minus the blending of identities since she does not have his memories.