Cockatoos and other parrots live in flocks in the wild also, but you don't see people telling them they have to have 2 of them because it's more natural and healthy. Just because lovebirds are small it doesn't mean it's different for them. If you pair a lovebird it's unlikely to stay tame. It's better if you are going to have 2 to keep them in separate cages. I think the name makes people believe they need a mate and that's simply not true.
If you did decide to get a second one I'd keep it in a separate cage and let them out together for play time.
Oh yes, I most DEFINITELY do see people telling others that even 'toos and 'caws, greys and 'zons and such should be at least two if possible, and I'm definitely the first to encourage anyone who's up for it to do so!
I mean, we're obviously from different parts of the world and I totally get that it's very unusual to have two big parrots together in, like, the US and the UK and stuff, and even here in Sweden you often see single birds (big parrots, that is - it's very unusual to have only one of the littles, from what I've seen), but there's also a lot of successful, tame pairs or flocks. Of COURSE it's the most natural thing ever for them to have partners/bird friends! Have you SEEN a cockatoo flock? Have you seen them play and forage together? It's the adorablest thing - and I'd LOVE for that to be possible inside our homes too. It obviously isn't, I mean, nobody could fit that many birds that size in their house, but why not do the next best thing, two birds and a couple of humans?
I TOTALLY get that that could be SOO hard to manage and I'm definitely not even close to judging anyone with a single bird, I just have a huge amount of love and respect for the ones who do give it a try or work it out!
The reason that I more often encourage owners of small parrots to try out and see if a partner would work, is that I know it's hard or impossible for most people to bring in another big parrot and then have it totally fail in one way or another. It's a huge responsibility and I'm not the one to tell anyone to take that big of a step, IF they're not telling me they're thinking about doing it.
Small parrots are easier to separate if things wouldn't work out one way or another.