LR deconvolution tries to optimise out the imperfections in the optical path, by analysing each star image know that it should be a pin-point.
Frow what I understand LR only works properly on "RAW" images. That is those that have had no jpeg (or other) compresion. With compression the optical information is generally lost, so LR is less beneficial.
However many have had success with LR's on Jpegs (iceman ext). It may be possible that remnants for the optical imperfections are still there and can still improve an image.
I have only tried LR on "RAW" images so can't really comment any further!
Cheers