How do you know she's lonely? Cats are usually quite solitary creatures and happy with their own company as long as their "human family" are around regularly to give them attention. You might find she resents another cat coming onto her territory now and a newcomer might find they have a very uncomfortable ride. Dogs, in my opinion, are more likely to enjoy each other's company than cats.
I have a cat. I recently had to move back in with my parents and they also have a cat. We kept them apart for a few days. My cat got used to the upstairs rooms and they became her 'safe space'. We then left them to fight it out between them . There was a lot of hissing and spitting but no fights luckily. They wouldn't eat together, pass each other or even look at each other. After about 3 weeks they realised they are not a threat to each other and get on brilliantly. They will eat side by side and quite often touch noses and lick each other. The only problem now is that my cat was always an indoor cat.... and my parents cat has shown her the 'dark side'.