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.
Here's a (partial) listing of the dependencies that were automatically selected sorted by download size†:
https://www.dropbox.com/s/950vm93v1ncna6x/lyx_synaptic.png?d...
So you can avoid a lot of your disk space usage by excluding‡ the -doc packages.
†: I haven't figured out how to get Synaptic to show estimations of unpacked sizes on a per-package basis
‡: In aptitude, `- .*-doc` I think?
Or, you have a third-party APT repository specified in `/etc/apt/sources.list{,.d/*}` that you didn't install the keys for.
Or the NSA.