Lighttpd is a web server more optimized for speed-critical environments, with very high traffic/requests or bandwidth. But it doesn't receive regular updates, and seems to be use for very particular requirements.
Litespeed is a paid web server, used most of the time to replace Apache, but it's a web server intended to be used by web hosting providers. But it is pretty expensive and billed on server size (CPU or RAM).
But if you are looking for the best web server, you should look on Nginx features, it can handle high traffic with a low resource usage and support the latest web technologies like HTTP/2 or TLS1.3.
Cloudflare use nginx on all their servers and they handle millions of requests and huge traffic.
Additionally Nginx support extensions and 3rd party modules, and you can customize it for your requirements.
Litespeed is paid one and is good for those who are having hosting business in which you may be using cpanel and needs integration with cpanel / whm to manage things .
You can use nginx as reverse proxy as well if you are having cpanel which will help to reduce the load of Apache server as nginx will be handling static files and apache will only have to deal with dyanamic contents.
If you are one having customised server then better try nginx as there is regualar updates, faster than other ones.
I have used lighthttpd in past but it do not have any integration with any control panel nor it is not that popular. In my last 9-10 years career, I have seen just 2 - 3 times who is keeping that only as they dont want to upgrade or change that as those are highly customised server environment
To define which one is better is more difficult! Both are well known web servers and being there for years. The main advantage with Litespeed is their drop in replacement nature with Apache which help people to switch to it without much hassle. Its Admin UI, integration with control panels, cache, etc helps to make it more popular among lighttpd over the years and I believe their solution did not disappointed their users so far. of course its a paid software and they have to serve their customers for what they pay for.
On the other hand, lighttpd is free and does not offer the level of integration/configuration ease like Litespeed. So far its being used in limited servers and not very popular in web hosting as well. Additionally you have to earn more knowledge on it to install,configure, manage and to get the support from their developers/users when needed.
Why you are not considering Nginx into the list?
That said, the term "better" is defined by not just its performance but also how difficult it is to maintain the stack based on your requirements and resources...