Is it permissible to lie to one's father about the price of an item to avoid extravagance, with the intention of returning the difference to him later?

Lying is forbidden. It can be avoided by using tawriya (equivocation) and ma'areedh (allusions) when there is a need to conceal the truth, such as saying, "This is sold for such-and-such," intending its high price. The difference between the real price and the price that was made known to the father must be returned, even if through a stratagem like a gift.