You don't mention how long you've had Lucy, nor what Lucy does that' not friendly with others in the household, but yes, Lucy would probably accept a second bird...sun conure or other, though it might take some time or they could hit it right off.
While Lucy has an attachment to you, a new bird would not, so it might take a while for it to accept everyone, and yes, new bird, new cage, though it would not need to be a large, fancy one.....would it be a mature bird? Would it be a mature bird, a rescue, a re-home or a young bird coming to a first time new home? Unless you want to deal with eggs & chicks, you might want to consider another hen.....won't preclude egg laying, but you wouldn't have to contend with chicks.
Whenever a new bird is brought into a flock, they should be quarantined for 45 days, unless you are familiar with the bird and its history.....not as related to you by someone else, but that you know the previous owner, the bird's health & that you are familiar with its attitude.....most people don't do this though.
Just because it's another bird...even another bird of the same species, that doesn't mean you can arbitrarily put a new one in with Lucy.....how would you feel if someone you didn't know moved into your room with you, so yes, another cage required.....at least until the birds decide to make their own sleeping arrangements.
Problems could range from standoffishness, to aggression.....you just have to wait & see.....if you do bring home a new bird, be sure to introduce the new bird to Lucy...there is a pecking order & Lucy being the resident bird, may be more tolerable & more accepting on a new one, because unless there's something wrong, she'll most likely assume a dominate roll with a new on & you introducing the new bird to her would help her establish her position.....