The former Celtic defender has been commenting in the wake of the Hoops' European defeat.
One of the big talking points coming out of the Hoops' UEFA Champions League exit on Tuesday was Lennon's decision not to play Boli Bolingoli at left-back.
The Celtic boss claimed prior to the match that his benching was due to fitting Olivier Ntcham into the team (The Scottish Sun).
However, the decision to move Callum McGregor to the left side of defence was seen as a major error, robbing Celtic of their usual tempo and effort in the middle of the park.
Now Stubbs has questioned whether Bolingoli was omitted because Lennon simply doesn't fancy the player.
As quoted by BBC Scotland, the former Hoops defender said: "It possibly raises questions about was, or is, Neil working that closely with head of recruitment Nick Hammond.
"If he [Bolingoli] has been brought in, then how much input has Neil had into that? As a manager you need to be working very closely to make sure the players that are coming in have your blessing and you are very comfortable.
"Because if it hasn't been Neil's signing, is that one of the reasons he's not got 100% faith in playing him in potentially Celtic's biggest game of the season?"
The suggestions from Stubbs should certainly be worrying for Celtic supporters.
If Lennon is not influential enough at Celtic Park to have a big say on transfers then what does it say about the future direction of club?
Having executives above a manager is nothing strange in football, but managers should at least be heavily included in first-team recruitment decisions and not, as Stubbs questions, a periphery figure.
Communication on the club's current strategy hasn't been very forthcoming and Celtic should move to offer a bit more transparency and reassurance about how things work.
The vacuum is being filled by speculation and fans deserve to know how the club plan to deal with their latest Champions League exit.
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