A computer from 15 years ago, cannot be expected to run a modern graphical operating system well. The fact that it runs at all is already very impressive! There is no magic wand that can make an extremely old (12 years is ancient for a computer, >3 years is already "old") machine run modern software quickly.
That said, while Lubuntu is indeed the lightest (and therefore fastest on old hardware) flavor of Ubuntu, it is still graphical and heavier than things designed to be ultra lightweight. So maybe (maybe) you would get slightly faster results if you try LXLE or another of the options listed in this random article I found.
At the end of the day, however, nothing is going to work perfectly. This is an old machine so you need to accept that it will be slower. Especially if you want to try running modern web browsers like firefox which are huge and require significant resources. You might want to try a lightweight, minimalist web browser instead.