There is no official statement about their relation other than the movie's content, but as that evidently has them have an arranged marriage, fall in love and have a child together - the answer is very likely an absolute NO. It's a Walt Disney cartoon and Disney is a kid-friendly company. It has no interest in promoting incest in any shape or form.
And it also must be remarked that even if real life lions inbreed, The Lion King movie lions are not real life lions but basically human: Real life lions don't have (arranged) marriages but humans do, real life lions don't fall in love but humans do. Real life lion pride's leader isn't bowed down to as a king and doesn't have human responsibilities and they don't raise their cubs the way Mufasa and Simba raised theirs, but humans do. Real life lions don't have royal blessing ceremonies for their babies but humans do. Real life lions don't mind inbreeding but humans do.
Cousins having a child together = incest.
Humans + incest = big no-no.
Disney lions = basically human.
Simba and Nala cousins/half-siblings = Never.
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Simba's (the lion king) wife is called Nala.Nala
Nala Nala
In the Disney movie The Lion King, Simba falls in love with Nala. She was his childhood friend. Several people told them when they were young that it was tradition for them to get married, but neither of them liked this idea very much. Until they grew up, that is. :)
The Lion King directors Roger Allers and Rob Minkoff stated during a Lion King 10th Anniversary Reunion that it could be either Mufasa or Scar. Despite this "canon" claim, Nala would be related to Simba and Scar nor Mufasa acknowledge Nala as their daughter in the film so the mystery of who is Nala's father is left up to fanfiction.
Nala