How long does a temporary lodger have to have lived in someone's house before they must be registered on the electoral register? What if the forms for the October register arrive before the lodger intends to leave (he plans to leave in November)? What if the lodger says that he is still registered at his old address with his ex-girlfriend even though he hasn't lived there for 5 months and he has no intention of voting?
There is no set period. Certainly 5 months with you would be regarded as 'permanent'. The fact that he plans to move is irrrelevant.
If he's with you on 15 October then you should register him. It doesn't matter if on the roll twice. It's voting twice that is illegal, not being on the register twice.
OTH if you don't bother to record him the chances of any comeback on you are just about zero.