Leaving luggage on the carousel is not a good method of storing it for a few hours!
Assuming you are arriving off an international flight into the UK you will need to clear customs with your luggage. If you leave it you can't just pop back into the baggage hall to reclaim it and pass through customs - there will be a (security) process to follow to gain access and that will take some time.
There are paid for baggage storage facilities at LHR which will cost you
£ 10 per item to store them for 2-24 hours.
As to 'spas in the terminal' I assume you mean an arrivals lounge in which case you would only have access to those if you are traveling in the appropriate cabin or have a high enough status with the airline / alliance you are flying with / are a member of. I know of no land side paid for lounges at LHR.