I think if the tick has gone he should be ok now; but he would do better to have the tests once he gets back to the States, just in case. We do have lyme disease here - where was he to have picked up the tick? Somewhere where there are deer? I think A&E would be unnecessary unless he is experiencing any neurological symptoms at this point.
Ds2 gets loads of ticks (we live near somewhere with lots of deer). The first time it happened I wondered about going to the docs but now I'm so used to it happening I am a bit blase. If your relative has removed it surely he would know whether it was a tick or not? I found some great pictures of ticks for another thread... here they are.
This site says it's unlikely that he will catch Lyme Disease unless the tick was attached for 24h or longer. And the first symptom is a rash which appears 3 to 30 days after being bitten. So I don't think it's worth doing anything right now. But that's just my opinion.