Goals after the break from midfielder Joe Ledley and forward Georgios Samaras took the Scottish champions into the play-offs 4-1 on aggregate and made sure they would at least get a place in the group stage of the Europa League.
The Hoops' squad fly out Philadelphia on Thursday to play Real Madrid in a challenge match at the weekend and the Celtic boss, who has only signed goalkeeper Fraser Forster so far, is hoping that during that time he will be able to persuade Lawwell to loosen the purse strings.
Asked if he could now go to his boss and tell him what he needed for the forthcoming European campaign, Lennon said: "It's a good question - I think you need to ask Peter that. We will talk about it over the next few days.
"We are going to America, which is so something for the players to look forward to. The players need a couple of days to recover and we will discuss things further when the time comes.
"We will see what the draw brings on Friday and we will give it everything we've got."