Their European adventure ended with a 2-0 defeat by Juventus in Turin on Wednesday night, 5-0 in total, and the 'boot sale' wil start in the summer.
One of the key players is former Newcastle goalkeeper, who is rumoured to be desperate for international recognition and his only chance is to play in the Premiership.
The key players who are most expected to move on are Forster, midfielder Victor Wanyama and striker Gary Hooper ... all looking to move to another level in their careers.
Lawwell told Sky Sports News: "I think inevitably there will be one or two players that will probably want to move on.
"But stability is a very important thing in football so we would hope to get the balance right, to make sure that there is some quality coming in that may replace those that are going, but keeping a real balance in terms of stability and continuity going into, hopefully, the qualifiers next July.
"It's been a great season so far. The Champions League has been wonderful - wonderful for Celtic and wonderful for the players and for Neil.
"Clearly, we are not naive enough to think that people won't be recognising that elsewhere."