Is it permissible to ask a client about the lowest price offered to them by other consulting firms and then try to offer a lower price?

You are not at fault for asking the customer about the lowest price he received so you can offer him an even lower price, as long as the matter is still in the bidding and price-discovery stage. There is no religious prohibition in that. The customer, however, must be truthful in his statement and not lie deceitfully, for the Prophet, peace and blessings be upon him, said: "Whoever cheats us is not of us, and deception and fraud are in the Hellfire."