The former Celtic and Rangers striker has announced his retirement from Scotland duty - with an exquisite goal at Wembley against England in last week's friendly marking his final contribution in the dark blue of his country.
Lennon played alongside Miller at Celtic Park under Gordon Strachan and he believes the forward should savour the highlights of his time on the international stage.
"Kenny deserved everything he got out of football," said Lennon. "I played with him and he sacrificed a lot for the team.
"He's one of the hardest-working players I have played with and a really good team player. He's had a great career and I think he's been a fantastic player for Scotland.
"There is no better way to retire than by scoring a 'worldie' at Wembley against England. I wish him well in whatever he decides to do."
Based in Canada now, where he plays in the MLS, it is believed Miller spoke to Strachan about domestic play-offs that could clash with forthcoming Scotland World Cup qualifiers against Belgium and Macedonia.
And it was decided this would be the ideal time for Miller to bow out of the international scene, with younger blood about to make the breakthrough.
Lennon added: "I suppose the timing is strange but with the travelling back and forward from Canada that he's doing now, it must be taking its toll on him. But he's had a great career at international level.
"Gordon Strachan knows Kenny well from his time here and there is a great trust and respect between them. He thought highly of Kenny by starting him at Wembley.
"Wherever Kenny has been, he has done very well and is popular in the dressing room. I am sorry for him that he's retired but he can look back on his career at international level with a huge amount of satisfaction."