Robertson, who can also play at right-back, enjoyed an outstanding pre-season for the Saints but suffered two injury setbacks which forced him to miss the opening game of the campaign.
Now the 24-year-old, whose current contract expires at the end of the season, wants to be the man Lennon chooses to replace the injured David van Zanten for St Mirren's home opener against Kilmarnock.
Robertson told the Daily Record: "I'm in the second year of my contract and the aim is to try to win another one.
"I'm happy at St Mirren. I enjoy training and being around the lads. If I can earn myself another contract from the gaffer I'll be happy.
"Fingers crossed I get a wee opportunity this weekend."