For your common, basic use case, the free versions of LastPass and Bitwarden are likely to be pretty much identical in function. They have similar free tiers. The biggest difference, and the reason I went with Bitwarden, is that they have free native desktop clients. I think LastPass does not have native desktop clients. However, I've since come to realize that's really not a huge deal because you can always open a browser on a desktop. I suppose there might be edge cases where Bitwarden's client could come in handy, like maybe you want to use it on a relative's computer but don't want to pollute their browser with plugins they don't use. It's a stretch, but it is a minor difference. On the other hand, LastPass is more common, and perhaps more concretely, I've heard the interface is a prettier and more intuitive. Bitwarden admittedly looks and feels like something a software nerd designed for themself. You'll probably have a slightly easier time picking up LastPass; at the very least, you'll find more search results for help and things like that. None of these differences are that big of a deal though.
Beyond the free editions, I don't know much about LastPass, but paid Bitwarden basically adds the functionality of something like Authy, where you can scan QR codes and use it for 2FA. As much as I wouldn't mind paying for premium Bitwarden to add that feature, I actually still use Authy separately because I want to have that functionality regardless of whether I continue paying or not. But it is a nice option if you want that all in one app. Back to the topic of Bitwarden's somewhat ugly but functional interface, it actually looks like this feature is available in the free version, but it sort of just silently doesn't work until you actually pay, which is kind of weird.
Another huge thing with Bitwarden is that you can host your own instance of it. In other words, instead of storing your private data with the company, you can actually host it yourself somewhere. This gives you a potential future alternative in case they get compromised or you have some other reason to prefer self-hosting, such as within a protected intranet. You likely won't use this for the foreseeable future, but I think it's actually a really cool option. Using LastPass obviously doesn't prevent you from ever switching over to self-hosted Bitwarden, but if nothing else, you'd be familiar with the web site and interface.