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 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."
Lambert added: "The cup run is exciting. It's given everyone the excitement that you're not too far away from getting to Wembley.
"We're going to have to earn it but it's exciting and you'd rather have it than not."
Lambert's biggest team conundrum concerns keepers Brad Guzan and Shay Given, who have both been in outstanding form.
Guzan has been the regular Premier League keeper while Given has played in the Capital One Cup and FA Cup matches.
Lambert said: "That's really hard that one, because the two of them are playing unbelievable at the minute.
"Brad has been excellent in the league and Shay has been different class in the cup.
"Would I swap them for any two keepers in the Premier League? Not the way they are, the two of them. This club is really fortunate that it's got two world-class goalkeepers."
Lambert has a stronger squad to choose from than of late with Darren Bent, Gabriel Agbonlahor and Charles N'Zogbia all involved after injury in the weekend FA Cup win over Ipswich.
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