Ellipsis again? Cool. It would help if we made a series of exercises with answers in order to practice it. Well, let's try this one.
I am not sure your suggestion is correct, because the pronoun 'that' is there.
If I understand well, the stuff should be omitted, not substituted by a pronoun.
We got a mortgage from the cheapest [house] lender.
After that, we made a [rent] offer on the house.
I am not sure I clearly understood the meaning of the sentence. were you trying to rent or buy a house?
What does exactly mean a 'mortgage' in this context?
We studied a similar example in linguistics. If my memory does not fail me, this case is substitution not ellipsis, because you have the word "that" referring back to "we got..."
Ellipsis occurs when there is no substitution for the omitted part. For instance: "The Elder sister was beautiful, the younger [sister was] more energetic." The bracketed part was omitted without a substitution. You can find more here.