The Southampton talisman made a fairytale international debut on Wednesday, scoring the winner against Scotland with his first touch while the Hammers star was out of the squad due to injury.
And Allardyce told the press: "I think there's a choice for that type of player between Andy and Rickie. It's going to be a challenge this season on who's the best of the two.
|6/1||Rickie Lambert is 6/1 with William Hill to score the first goal in West Brom v Southampton
"I think it will be a competition between the two on who consistently plays the best this season. From a selfish point of view, I hope it's Andy."
Lambert scored within three minutes of coming on against Scotland, later hitting the woodwork and forcing Allan McGregor into a fine save from point-blank range. Allardyce was delighted for the 31-year-old, who has risen from the bottom of the Football League to international level, arguing that every squad needs a player of his type.
"For Rickie it was great to see him come on and make a statement," the West Ham boss added. "To get the winner against Scotland shows what he can do and what England might be missing a bit.
"It shows you have to have other dimensions in your squad no matter what level you play at."