Most certainly. LibreOffice is Free Open Source Software, and you are free to download the source code and do what you want with it (source code). In fact, we encourage you to do so. If you're a coder, maybe you'd like to develop extensions for LibreOffice (for that, you can download the SDK). If so, we invite you to contact the developers team and get involved with core development.
To do that, go chat with our devs on IRC, or subscribe to the developers mailing list and introduce yourself. There are devs working 24/7, and they are friendly and perfectly willing to help you get started.
If you're a less-experienced coder but would like to get involved and learn, we have a special category of tasks you can easily start with: they're called "easy hacks", and are various jobs you can do without too much knowledge of programming and the code base - things like cleaning-up comments and defunct code, etc. They're immensely useful contributions, and you'll familiarize yourself with the code while you're working, with fostering and help from our more-hardened veterans.