The Yorkshire batsman was dropped after seven appearances in 2015.
But a brilliant start to the season has reignited his hopes of an England recall.
“I do feel I’ve got unfinished business at that level,” said Lyth, who is the leading English run-scorer this season with 488 from the first three County Championship games.
“Obviously, the more runs you get the more people will talk, and hopefully that continues in the coming weeks. All I can do is keep the runs coming and keep putting my name in the shop window. If anything happens, it happens; if it doesn’t, then I’ve just got to keep scoring as many runs as I can.”
Lyth, 33, was one of a number of players tried and discarded as England sought a replacement for Andrew Strauss.
Lyth scored a century on his second Test appearance against New Zealand at Headingley but struggled in the subsequent Ashes series against a highly-talented Australian attack.
In recent times, the likes of Rory Burns, Dominic Sibley and Zak Crawley have all played well at various stages without suggesting they are better than Lyth.
Now with Lyth arguably in the form of his life, scoring runs not only in volume but with eye-catching fluency, he deserves to be strongly considered for the international season that starts in June.
“Obviously there are some good players out there and all I can do is keep trying to bang the door down,” said Lyth. “I haven’t consistently stacked up the runs I’d have liked in the last couple of seasons to have been talked about (for England), but this year I seem to be hitting the ball as well as I’ve ever done. I’m definitely not finished (in terms of international cricket), and if I do ever play again (for England) I feel that I’ve got that unfinished business.
“But time will tell and, like I said, all I care about is scoring big runs for Yorkshire and whatever happens, happens.”
Since returning to action from a calf injury that curtailed his involvement at the Pakistan Super League, Lyth has been in stunning form. He hit 52 and 50 retired out in the final pre-season friendly against Durham MCCU at Headingley before starting the Championship season with 52 and 115 not out in the Championship opener against Glamorgan at Headingley. Lyth followed that with 97 and 116 in the win against Kent at Canterbury and 42 and 66 against Sussex at Hove.
He likens his purple patch to some of the best form of his early career, which helped to put him on England’s radar in the first place, having worked on his trigger movements during the winter with former England coach Andy Flower.
“In terms of comparing my form to years gone by, I’d probably liken it to 2010 and the early 2014 season,” said Lyth, who hit more than 1,500 first-class runs in both campaigns. “But you can take nothing for granted in this game; you can go two or three knocks and not get any runs, so I just have to keep playing the way I’m playing.”