I've read through https://www.latex-project.org/lppl/lppl-1-3/ but I still don't really understand how this licence works. Can I use the "work" under this licence in a commercial product?
What is the license on the original set of word patterns?
Just pre-compiling a LaTeX file to speed up it's use, should not put the output under the LPPL.
In other words if you are the creator of the original file before it was pre-compiled, you can use it how you wish.
Normally the LPPL is used for projects that want to make sure that programs distributed under a name/version are identical to each other. In other words you can't distribute something claiming be "XXX" unless it is identical to the orignal "XXX" distribution.
This also means that if that pre-compiled file is part of another project that is licensed under the LPPL, you can not just include that single file unless there is another license that applies to its distribution. On the other hand you could distribute the entire project, but only use certain files from it in your own project.