Well thats a first lol, a Lab that is not greedy! I thinks its a case of teaching him to retrieve rather than just throwing things, i.e. you have to teach him to 'hold' whatever it is you want him to fetch, and to 'give' it back to you on command.
You do this by placing it in his mouth, making sure it something he can easily hold and pick up, i.e. a long soft item, hold your hand under his jaw to keep it closed (very gently) and once he is happily taking it from you and holding it for a while and then following your command to 'leave' or 'drop'dropping it back into your open hand you can progress to placing it on the floor and asking him to 'hold' or 'take' it whichever command you use. Then you can throw or place it a distance away, and take him on the lead and give him the command hold or take, and when he picks it up run backwards a few paces and encourage him to follow you, but be ready to quickly catch it if he drops it. This then leads to him coming back with it and sitting in front of you when you can give him the command leave or drop.
This is of course one way we teach an 'obedience' retrieve
but if you don't want to go down the formal route, then its just a case of hoping he will one day get the idea, but some dogs will never retrieve even if its what they were bred to do. Anyway, you will no doubt have lots of fun trying!