The Parkhead chief yesterday unveiled Ronny Deila as the new Hoops boss.
The Norweigan will spend the coming days and weeks casting an eye over his squad as he prepares for the Champions League qualifiers.
And Lawwell, who confirmed keeper Craig Gordon is on the Hoops' radars, is determined to hold on to top talents like Fraser Forster and Virgil van Dijk this summer.
He said: "We are in a position where we don't need to sell. We don't want to sell. But these things normally sort themselves out.
"The frank answer is that we can say what we want, that we don't want to sell a player and we want him to stay. But if someone offers a player four or five times their salary then it turns their head and things become a little more difficult.
"We have said to Ronny that we don't have to or want to sell. But there is a reality out there that we might have to face. We hope not, though.
"We will work the same way that we always have in that the manager has the final say on all players coming in or going out, or their stays being extended."
As well as tinkering with the Hoops squad, Deila will have to appoint an assistant manager, with John Collins one of the names in the frame.
Lawwell said: "There are three or four candidates. Ronny has confirmed he (Collins) is one of the candidates so we will wait and see.
"I think we need someone who knows what Inverness is like and the trip up there at 12.15 on a Sunday, who knows Scottish football.
"I think that would be a big requirement for a No.2. We need to really start that process."