It is so big because it is based on Latex and its ecosystem, which is on most distributions by default quite large. It will install a lot of Latex packages which you probably won't need right away, but if size isn't a big problem I wouldn't bother with trimming it down.

One of the advantages of Lyx is that it builds on Latex and its extensions, which thanks to tens of years of development is very mature and feature rich. If something that you want to do with Lyx isn't supported you can just use raw (La)tex script. For example I used it for autonumbering of chemical compounds.