I have recently obtained a mortgage that I don't like the terms of
(papers signed and dated).  The lender says that they need information
(copy of the Setttlement Statement ... HUD) of a prior condo sale that
I made earlier this year.

If they don't get a copy of this for their records, what might happen to the loan?

Papers signed and dated?
Sounds like the personal loan I got and they held the car as
collateral. A month later they call asking for the proof of collision
coverage. I said "No way, Jose." And there was nothing they could do
about it.
That's my opinion, of course, but you should read the terms of what
you signed. Does anything in there state that the mortgage is on
condition of you supplying paperwork X, Y, or Z?

They forgot to request the document and now its at closing and their
Quality Control people picked up on the mistake. Its serious enough
for most lenders to abort the loan especially if they sell their loans
following the closing. If they keep the loans and don't sell then they
may choose to close and do the loan but I doubt they keep them. Almost
all sell on the secondary market and they would get grief from the
buyer. They would consider it not worth the brain damage.

That said they may if they are smart get a copy from the previous
escrow co. You better call the escrow co. and tell them not to release
this document to anyone to be safe;)

Also..there is a 3 day right of recission on the loan.

Maluca has a basic understanding of the loan process, however....
Why are you concerned about holding the HUD-1 from your prior sale
back? While it is true, that they should have had that documentation
in the file prior to funding the loan, the fact that they have
requested it after the fact shouldn't make you afraid of something
underhanded. This documentation is needed to prove that a large
deposit made to your account was due to a prior sale, or that you do
not any longer own the condo, therefore the debt-income ratios are
correct, or that money that you put down on your new purchase came
from "seasoned" funds, that is money that you have had at least 3 mos
or more.
There can be no harm to you by providing this document. When loans are
bundled and sold on the secondary market, they are guaranteed to
perform to a specified minimum standard, for example, all loans are at
80% LTV or less, or that they all conform to FNMA standards, or
whatever type of loan that they happen to sell.
By you not providing the HUD-1 to your lender, you prevent him from
selling this loan on the secondary market since it does not have all
the necessary items in the file. Lenders need to sell their loans to
FNMA (or whoever) in order to be able to make more loans in the
future. That is their business. And the longer they hold on to your
loan, the more money they lose. Not fair to them.
They made you the loan that you requested, you should now provide the
necessary documentation for them to proceed.
And, by the way. You did not specify if this was a purchase loan, or a
refi. If it is a purchase you do NOT have a 3 day right of recission,
that only applies to a refi. You also did not mention why you are
unhappy with your loan???? Maybe it is not as bad as it seems....

The reason why I am not happy with the terms of the loan is that they
are not the terms that I requested.   They changed the terms on the
day of the closing (or at least they did not inform me that they
changed the terms and they were different than the terms I requested
... and I did not know of these changes until the day of the closing).
  I could have walked from the closing table, but there was a lot at
stake, and made the decision to close that day.