Manager Neil Lennon admitted it would be difficult to keep his squad together following their run to the last 16 of the Champions League, after their European adventure ended with a 2-0 defeat by Juventus in Turin on Tuesday night.
The key players who are most expected to move on are versatile midfielder Victor Wanyama and striker Gary Hooper, who attracted several bids from Norwich in January and is approaching the final year of his contract.
But Lawwell is keen to ensure that Lennon can hit the ground running when Celtic's next Champions League campaign begins.
As such, he does not look like sanctioning widespread departures - and promised to provide adequate replacements for those that do leave.
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."
Lawwell also recognised that his manager's stock has risen from their run to the knockout stages, despite a 5-0 aggregate defeat by a clinical Juve side.
Lawwell said: "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.
"If he keeps progressing and being successful, I'm sure he will be courted at some point.
"But Celtic is a big part of Neil Lennon and maybe he won't be able to get elsewhere what he gets here at Celtic.
"We are hoping that he stays for a long, long time."