The Bantams pulled off a shock win over Arsene Wenger's side in a penalty shootout in the previous round.
The scenario is different for Villa, who have a home second leg in a fortnight's time to recover from any potential setback, but Lambert knows they cannot take the npower League Two side lightly.
He said: "I've managed at that sort of level and I know exactly what it's like, and I know what it's going to be like there.
"That's why I never underestimate any game and you've got to give Bradford a lot of credit for what they've done.
"Everyone outside will assume Villa will win - the same as everyone assumed Arsenal would beat them - and when you don't do that, it becomes a huge thing.
"That's why you never take it lightly. The players will know themselves what they're going into.
"The beauty is you've got two cracks at it but it's going to be really tough, because Bradford have absolutely nothing to lose.
"Whatever way you look at it, they've gained a lot of credit and a lot of plaudits, so we have to be ready for this game."