The Hoops' boss, who played with Miller at Parkhead in season 2006/07, won the Clydesdale Bank manager of the month award for September after another three SPL victories extended his winning run to six out of six and kept Celtic behind their Old Firm rivals at the top of the table only on goals scored.
Miller, in his second spell at Ibrox, has been the main factor in the Light Blues' good start to the season with 10 goals in six SPL games and today he picked up the sponsors' player of the month award for the second successive month.
Asked if the Parkhead club had perhaps got rid of the Scotland striker too early, the Celtic boss replied: "I can't answer that because I wasn't the manager at the time but he was a good team mate, I know that.
"Every goal he got he deserved because he was a good team player.
"He always got in the position to score goals and you always felt that if he kept doing that the goals would come.
"He is a bit more experienced now and has probably found he doesn't need to run about as much although that comes naturally to him.
"And he has found a level of consistency in his finishing.
"I think he has been quoted as saying it's the best spell of his career so he deserves it - but I hope it doesn't last too long."
Celtic welcome Hamilton to Parkhead on Saturday and Lennon accepts that most fans will be expecting to see their seventh successive SPL win of the season and with perhaps something to spare.
The former Hoops' captain said: "It's a no-win situation.
"If we win we are expected to win and if we don't then you are going to take criticism for that.
"But we are confident and are pleased with the way things are going but that can change in one game and with one result."
Looking further forward to the inaugural Carling Nations Cup, Lennon appeared lukewarm to the prospect of losing players for the first round of games scheduled to be played in Dublin in February.
The fixtures were announced today with the Republic of Ireland playing Wales on Tuesday, February 8 and Scotland playing Northern Ireland the next night, with two more rounds of fixtures at the end of the season.
The former Northern Ireland midfielder said: "It depends how we are going and how well the players are feeling at the time but I wouldn't stop players going, I think it's important.
"I am pleased that Shaun Maloney has been called up to the Scotland squad this week, I think he deserved it.
"It will be competitive which I suppose is not a bad thing and it might generate a bit of public interest.
"But from my point of view, at that stage of the season I would probably be wanting my players to have the time off.
"It's probably one that club managers would prefer to do without.
"But we don't dictate the international fixtures, and we can't stop countries calling up our players, it's something you have to put up with.
"But I will cross that bridge when I come to it."