The 31-year-old scored on his debut against Scotland before doubling his tally in an England shirt in Friday's 4-0 victory over Moldova which helped propel the side to the top of Group H on goal difference.
And Lambert is confident he can lead England to victory despite the absence of Wayne Rooney and Daniel Sturridge through injury.
“Whatever the gaffer’s plans for me on Tuesday, I’m confident,” Lambert told reporters. “Whether that’s starting or off the bench, I’m confident when I get a chance, I’ll put it away.
|80/1||Rickie Lambert is 80/1 with bet365 to score a hat-trick against Ukraine
“The game on Tuesday night is another chance to impress. Getting moments like Friday night, I want more now, I want more.
“We understand it will be completely different in Ukraine, but we’re in a good place at the minute and the boys are really confident, and there is a feel-good factor around. We’re looking forward to it.”
Hodgson has total faith in the Southampton frontman, who was playing in League Two with Rochdale just seven years ago, and believes he is well-equipped to lead the England attack on Tuesday.
“I don’t have any qualms about it,” said Hodgson. “The fact is Rickie was selected to play against Moldova because he merited it. He did well enough to justify the selection.
“If you play well in a game and justify the selection, you are entitled to think you will continue. Qualms would definitely not be the right word, even though we can’t deny either that the competition for places at centre forward has been diminished enormously.
“The most important thing for Rickie is to feel confident and feel he has the confidence of the coach and the coaching staff, and to feel the players have confidence in him.
“You don’t see anyone not wanting to give him the ball. I have not seen any sign, since he has been in the group, of him not being very well integrated. We have a very good group of players.”