I am looking into setting up a survey that uses respondent-driven sampling. In this scheme each respondent is given the opportunity to refer up to a fixed number of friends to take the survey. Each new respondent would complete a survey that includes a question at the end to input 2 email addresses. These email addresses would then be given unused tokens and emailed invitations to complete the survey.

I can certainly do this manually, but with many hundreds of survey participants I much prefer going the automated route if possible.

I have done a fair amount of reading and can't seem to find the answer to this in the LS documentation. Any suggestions would be much appreciated, thanks!

There is no built-in option for doing it. Although you can create a custom script that reads the e-mail addresses directly from database and sends an invitation through LS Remote API ( manual.limesurvey.org/RemoteControl_2_API )