The Wales international, whose current deal is up next year, scored twice, with a penalty from James Forrest and goals from Dylan McGeouch and Gary Hooper completing the rout.
"Ledley was great and deservedly got man-of-the-match, he is a very important player and proved that over the years," Lennon said.
"He is talking about staying on here and I would like to do that if I could, he is a great player for us."
Celtic are a formidable outfit at home and the win stretched their advantage at the top of the SPL to a formidable 21 points.
Lennon added: "We weren't great in the first half but in the second half we were excellent and I am really pleased with the five goals.
"That's 23 goals in the last five home games so we are really starting to turn it on at home.
"I was pleased with Dylan, it was a great goal and that was our fourth or fifth penalty in a row (we scored) which makes a nice change for us.
"Gary got his goal which puts him on 24 for the season, so I was delighted with the performance and the clean sheet."
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