Need first to see what exact Mac model you have. Also, note Lightroom's system requirements:
Your computer must meet the minimum technical specifications outlined below to run and use Lightroom.
helpx.adobe.com
So, Mojave, OS 10.14, will do just fine. With that, you'll only be skipping one version of the Mac OS when you upgrade.
A number of folks on here are quite pleased with Mojave, so you'll be getting a solid Mac OS.
Now, if instead you want to upgrade to either Catalina or Big Sur, there is the issue of 32 bit software. If you have any, they will not run on either Catalina or Big Sur. You'll have to try and find replacement software for them.
Also, Big Sur is not that stable yet, along with the issue of software compatibility with Big Sur (not an issue with Lightroom, but could be if you are using other third party software).
Finally, given that you will need to skip over one or more versions of the Mac OS, it is better if you do a clean, fresh installation of the new Mac OS you are moving to.
But first need to know your exact Mac model. And there is the possibility of needing firmware updates, as hallux pointed out above.