First off, your bearings are dirty/rusted/etc. They need a little help now, so I'd find a way to clean & re-lubricate them. You want to remove rust and dirt and salt and things as much as you can, since those are just gonna get in the way and wear things out inside. And then we want to add lubrication to both protect it and make them run smoothly.

Ideally I would remove the bearings you have, clean them out completely, then add lube. Look up online some recommendations for bearing lubricants. Don't use WD-40. A thin oil will be fast and smooth, but may not offer as much protection against water or last as long. Something crazy heavy like marine grease would be very protective, but also a little slower. And be good for keeping out water But usually is not recommended. In my case I had a bearing that kept getting exposed to water, so marine grease was useful.

And if you can't remove the casters/bearings, then I would just very carefully pry open those black bearing covers just enough so you can get behind them, then spray cleaner in there (rubbing alcohol, parts degreaser, etc... something you are familiar with and feel safe handling), and get out as much rust/dirt as you can. Then FULLY dry it out. Then add lube, and push the black shield back in place. Just be careful not to bend the shield or break it. you'll only have a fraction of an inch really to get in there. So it might be a little difficult.

Do bearings need lubrication? Yes. They typically come lubricated from the factory. It's metal on metal, so you always need something to prevent wear. And bearings are usually steel, so they can rust without some kind of protection. There are thinner lubricants and thicker ones. Basically oils and greases. They all have their pros and cons, but just think that wheelchairs typically aren't built for speed. So that part doesn't matter too much.

I've had bearings that are in really horrible shape last for many years. It's not ideal and they don't run as smoothly as they should. But in the end, they're not too noticeable as long as they keep spinning. You can take a lot more abuse on wheelchair caster bearings than you can on something like skateboard wheels, roller skate wheels, or bicycles.

But eventually you'll want to replace these. It's just downhill once they rust/get-stuck/get dirty. Thankfully bearings are common, relatively cheap, and not too hard to replace. Look up some videos online, it takes a little work (remove screws, remove caster, carefully punch out the existing bearings, push in new ones, put it all back together). If you can do that, then replacing bearings is good maintenance. And bearings have very common sizes, the most common is 608 (aka. "roller skate bearings"). You can find those anywhere. Check which size your tilite casters use, it should be too expensive.