Like Joffm: There is a setting to anonymize the IP address, which will get rid of the last part of the IP address.
I collected the IP address during the survey in order to filter out duplicate answers (people can circumvent the LimeSurvey cookie with another browser or in inkognito mode).
I don't think that the IP helps much either. Most people today have very easy access to at least two IP addresses.
Where I am right now, I have access to 3 different IP Addresses, without a big effort (two different fixed internet connections plus my mobile connection). Then there is the connection at home. So if someone really wants to take part in your survey more than once, the IP address is basically as easy to circumvent as the cookie. So while it might stop some, I don't think it is a very good measure.