You could install
Piwik Analytics
and setup some tracking URL's which you can use on the end URL link.
Or maybe you could use Google Analytics instead, however Piwik is more user-friendly and you can install it to your own servers instead of having it linked to Google.
Where I work we use Marketing Town, however that is only because we use their services for many other things (it's £500 a month, so I doubt you'd want that, just go with Piwik).
And you should keep in mind eventual privacy issues. For research you usually guarantee a certain level of confidentiallity (either because of your own policy, because of rules that certain organizatins like ESOMAR imply or because of legal requirements).
So you need to think about what you really need/want. I would assume that you only want to count how often a certain link has been clicked? Using Piwik for this (which is actually a very good tip from Krypsin), might be overkill, depending on what you try to do and what it is for.
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Provide your LS version and where it is installed (own server, uni/employer, SaaS hosting, etc.).
Always provide a LSS file (not LSQ or LSG).
Note: I answer at this forum in my spare time, I'm not a LimeSurvey GmbH employee.
Yeah Piwik could be a bit overkill to be honest, as you said it depends on what you're looking for.
If you're not fussed about fancy analytics graphs and statistics like browser usage, geo-locations, referrals to links and other stuff then there are plenty of free PHP scripts you can find on Google.