Unless you purchased a copy of Lion from the App Store you are unlikely able to access Lion today. Lion was the last paid version of macOS.
A couple years ago I saw an older article on one of the major Apple fan sites which mentioned how to acquire the installer while booted into Internet Recovery Mode so you could create your own USB installer for an outdated OS. The article was referencing an OS that was no longer linked by Apple (I think it was Mountain Lion, but the technique should work with any OS that can be accessed by Internet Recovery Mode). Unfortunately I don't recall the details although I may have it bookmarked somewhere since I was curious about it. I don't think your Mac Pro supports Internet Recovery Mode.
However, a lot of users on these forums have reported issues attempting to install Lion while booted into Internet Recovery Mode (laptops). While there may be some third party apps which try to create a bootable macOS USB installer most times I just see people complaining that those installers created with those third party apps don't work/boot (Apple made some changes to the installers a couple years ago).
Unless this Mac Pro can have its firmware updated to accept a later version of macOS, then I really think Snow Leopard is your best bet if you can find a retail DVD version of Snow Leopard (not the gray disc made for one very specific Mac). Posting your OS questions about macOS & Windows in the Mac Pro forums will get you contributors that are much more knowledgeable about the possible options available for this Mac Pro especially to know if it is possible to install a later version of macOS on it.
If you are willing to learn a new OS, then installing Linux on this system is most likely the best option to have a current OS with support for the popular web browsers (Firefox, Google Chrome, Vivaldi) plus Linux has access to lots of free open source apps. Linux definitely isn't for everyone, but it is a great way to extend the life of an old computer. I was still running an old (15+ year old) Dell 32 bit laptop up until two years ago, but I was concerned that I would no longer have a web browser. My fears were premature since Vivaldi still has a 32 bit browser available and the next version of Debian (v11, aka "Bullseye") still has a 32 bit OS available though I'm not sure how many more version will have 32 bit support (it is one of the last major Linux distributions to still have a 32 bit version).