If you are paying a low interest rate on your mortgage, say 4%, you would make more money investing your lump sump in a higher rate account - this depends on whether you are a tax payer, if you pay mortgage protection and so on.
It is not straightforward. Excellent independent advice here:
The general situation is that when you have a mortgage your deeds are stored by th ebank which you have the mortgage with, once the mortgage has been paid you need to pay somebody to store the deeds. Therefore people keep a very small mortgage so that they don't have to pay for the safe keeping of the deeds.
However I think that is no longer valid as deeds are no longer a physicall thing as they used to be.