Me and my girlfriend flew HNL - LAX - LHR - HEL with 12h layover in LAX and 6h layover in LHR, so I asked the HNL - LAX AA flight attendant if we could take the (economy) blankets with us. HNL - LAX was a redeye and we didn't sleep much on that flight and we were planning on sleeping in the lounge at LAX. Flight attendant gave us the permission to take the blankets, but don't know how much it affected the situation that I was Exexutive platinum at that time and had talks with the attendant about our long journey back to Finland and the long layovers that we had.
So long story short: Asking is ok, stealing is not. And yes, the blankets helped quite a lot the sleeping in LAX lounge, LAX - LHR flight, LHR lounge and LHR - HEL flight. Rough trip