After 3 years of working at my current company I decided to leave for a new job. My notice period for my current employer is 4 weeks but I told my new employer it was 6 weeks to give me some time off. After giving in my notice to my current employer it turns out he is close friends with my new employer. I am concerned that they will discuss the discrepancy between the 2 different periods and the potential fall out from this. Should I be worried? Is there anything I can do now?
It was rather silly to lie and it was completely unnecessary.
Instead, you should have just told your new employer when you would like to start and avoided any lies. Taking just a few weeks off in between jobs is very common.
Unless these are two very small companies and you have a very prominent role in both, the two friends are unlikely to bring your name up.
That said, avoiding a lie in the first place is almost always the best course of action. Now, you need to be prepared with what you will say in the off chance that your new employer catches your lie. Perhaps something like "I'm embarrassed to admit that I just wanted an extra two weeks off." would work.
In the future, instead of talking about 'notice periods' to your new employer, talk about 'time before you're available'; you won't need to 'lie', it'll be generic enough to cover the notice period and the time you want to take to prepare for the new job.
Now with the issue at hand, I would not worry about it.
I would think that your new employer would be smart enough to understand that you wanted to take a break before starting the new job. It may be different for you but, where I live, vacation time takes time to accumulate and you'll have your next vacation in one year from your first day at the new place.
If the subject ever comes between you and him/her, just be frank and tell them you wanted to get some rest in order to be fresh, ready and primed for your new challenges. You can also mention that it had been a while since you had a 'real' vacation, if it's the case.