My Problem: I had a UK driving licence (year 2000) and travelled a lot since ( Europe) so no UK address, now I lost my licence and I am kind of homeless. How can I get my UK driving licence without having a UK address. Thank you for your help.
UK drivers licenses can be replaced, even from overseas, but only if the applicant resides in Great Britain. See this UK govt page on getting a replacement license, which contains this text:
Get a replacement provisional or full driving licence online with DVLA if yours gets lost, stolen, damaged or destroyed...
...To replace your licence you’ll need to: be a resident of Great Britain (there’s a different service in Northern Ireland), not be disqualified from driving for any reason pay £20 by MasterCard, Visa, Electron or Delta debit or credit card provide addresses where you’ve lived for the last 3 years.
Thus, to replace your lost license, you'll have to lie to DVLA about your residence. None of us would recommend that course of action.