The winger scored his first goal since August 2016 in the 4-0 victory over Bournemouth, producing a clever finish to put the Clarets two up and well on their way to a first Premier League win of the season.
Bournemouth were almost certainly the reason Southgate was at Turf Moor after their flying start to the season but Burnley's home players will have done their international causes no harm, in particular James Tarkowski and Joe Hart.
Lennon, now 31, made his England debut as a teenager but has not been capped by his country since February 2013.
He said: "It's a long time since I played international football.
"You never know. But the only thing I am concentrating on is playing well for Burnley. Whatever happens, happens."
Lennon has been rejuvenated since moving to Turf Moor in January, playing a key role in Burnley's seventh-placed finish last season.
He found himself the target of frustration from the Burnley fans against Wolves last weekend but was firmly back in favour for his performance and goal on Saturday.
He said of his goal drought: "It's been preying on my mind to be honest.
"I should score more. I've had a few chances this season but it is great to get the goal.
"If you are playing every game you want to aim for double figures. But for me getting assists is just as important. It makes my day if the other lads score as well.
"It didn't matter how we won. We knew it was just important to get back to winning ways. To win 4-0 was even better.
"We worked on it all week, getting back to basics, being on the front foot and doing what we do. From minute one we were in their faces and it has paid off for us."
The three points lifted Burnley off the bottom of the table and, after calming early jitters, Lennon sees no reason why Sean Dyche's side cannot be a factor again at the right end of the table this season.
He said: "I don't see why not. The squad is pretty much the same, we've brought in a few quality players, as you can see, and obviously we're out of the Europa League now and we go back to one game a week so we get to work on the training pitch and hopefully we can kick on from there."
The emotions were rather different in the Bournemouth camp as their fine start hit the buffers, and full-back Adam Smith bemoaned the fact his side were outfought.
Smith said: "We'd had a good start to the season and we wanted to build on it. Burnley play to their strengths and fair play to them.
"We didn't do the dirty side, and we got punished for it. We let them get crosses in and we didn't even get the second balls on the crosses there.
"It was just disappointing that we're not doing the rough side of it. We can do that side of it but it's about doing it at places like this."