Stealing from shops I always took mine back to shop. Lies my 11 and 8 yr old do it still. I do make a big thing about it and punish much harder than what it is they are lying about. So if there is a clear punishment say going to bed early for stealing chocolate from sister then the punishment for lying about it would be to go to bed early for two nights on the trot. That way it's easier to admit to the actual theft than the lie about it.
Mine go through phases and won't lie for ages and then get away with it and so start to lie all the time until they get found out. Then I come down hard on them and it stops for a while.
Nothing much else to add as both of mine still do it so maybe not the best person to take advice from.