A number of Championship sides had expressed an interest in taking Given on loan, but the club insist that Given is staying at Villa Park.
Asked if Given would be allowed leave on loan, Lambert said: "No. Shay, in the games he's played has been excellent.
"He kept us in some of cup competitions to be fair to him. Brad has been playing ever so well himself. I've said it before, this club is fortunate to have two great goalkeepers."
Meanwhile Lambert hopes striker Andreas Weimann will commit his long-term future to the club after confirming talks have opened about a new contract.
Weimann has been one of the few plus points in a dismal season to date for Villa and he is their second top scorer with nine goals behind Christian Benteke.
The Austrian international still has 18 months to run on the deal he signed in August 2011, but Villa hope he will remain as part of the rebuilding process under Lambert.
"For the long term it would be great (if Weimann signs a new contract)," said Lambert, who was speaking ahead of tonight's crucial Premier League relegation battle with visiting Newcastle.
"I know the club and Andreas are talking at the moment so we'll see what happens there.
"But he has played really well and his goalscoring this season has been excellent.
"He is without doubt a natural finisher and he's done really really fine."