As far as the discs themselves go, I don’t think there’s much you can do except complain to Lovefilm.com about the damage sticky labels can do (one of the sticky threads in our CD & DVD Labelling and Printing forum could be of help there if they require further reading).
Having said that - you don’t say what model your drive is. This could be helpful if a firmware exists to slow down read-speed (long shot, but there might be one).
Or another option would be to either bite the bullet and get a standalone, or start renting from somewhere else
Hopefully other members can offer help or suggestions as well. Welcome to the forum
Although this isn’t strictly blank media related, I’ll leave the thread here, as there is a lot of knowledge regarding sticky labels here.