A Lions tourist in 1997 and 2001, Catt helped Irish reach the Guinness Premiership Final with yet another impressive performance last Saturday.
The 37-year-old claimed a vital try and controlled proceedings masterfully during the 17-0 win over Harlequins at The Stoop.
And, with Lions head coach Ian McGeechan highlighting the importance of current form for the 10-match tour of the Republic, Booth believes that Catt could be just the man to help the tourists return to winning ways.
"Mike Catt was absolutely outstanding. He should be going with the Lions," claimed Booth.
"From what you saw against Harlequins at the weekend, find me someone who's better. I can't speak highly enough of him.
"The irony is he spent two days in bed with flu. We still started him because we know how important he is to controlling things.
"Catty has a fantastic appetite - people dream about being able to do what he does at 37. He's a credit to himself, his family and London Irish."
If Catt does receive a call up from McGeechan and his fellow Lions coaches, he would become the oldest player ever to be included in a Lions party, taking over from fellow World Cup winner Neil Back.
The tour to his homeland could also provide the South African born centre cum fly-half with a dream send off if he does as expected and retires from the playing side of the sport prior to the start of next season.
"It's Mike's decision whether he will play next season," added Booth.
"I'll never ask him to stop playing. If push comes to shove I'm sure he'll put his hand up because that's the sort of guy he is.
"Mike loves the situation he's in and he'll make the decision over the course of the summer."