Female lycans can and do exist, although we have only seen a few of them. Any human, male or female, bit by a lycan will either die or become a lycan themselves.
Out of universe
I am not aware of a statement from the film creators about the lack of female lycans in the first four films. For Underworld: Blood Wars, however, we have this quote from Kate Beckinsale in a Q&A about Blood Wars on Facebook (7 minutes into the video):
Question: Will there be any female lycans?
Kate Beckinsale: Well, here’s the thing: the advantage of having a female director is that she was quite concerned about the whole fact that the female lycans always seemed to be at home making dinner and not actually on screen. So yes, there are female lycans.
Blood Wars is the first time that the franchise has had a female director.
I saw at least two female lycans in Blood Wars, both visible in this screenshot from the third trailer:
Still, two women and dozens of men is quite a skewed ratio. To explain this, we need to consider the history of the lycans.
Lucian was the first lycan. For the first 200 years of his life, all lycans lived in captivity in Castle Corvinus. They served as daylight guardians for the vampires, and we also saw them performing construction work. Viktor forced Lucian and his progeny to feed on humans in order to create more lycans. As such, the gender distribution of the lycans was entirely up to Viktor. Given that their duties mainly required physical strength, Viktor may have preferred to turn only males.
It's possible that there were female lycans doing other tasks around the castle while the men were doing construction work and guard duty, but we have no evidence of this in the film or novelization of Rise of the Lycans.
It's also possible that Viktor avoided creating female lycans because he wanted to avoid the possibility of the lycans interbreeding, but again, there is no proof of this either way.
After the escape
After the lycans escaped Castle Corvinus, they were in a constant state of war with the vampires. Female soldiers have historically been rare, so it appears that either Lucian's army preferred to turn mainly men to join their ranks, or few women agreed to join them. Although the lycans had at least one scientist, nearly all of the lycans that we've seen in the films are warriors.