You grandmother might have to pay gift tax on the equity.

It either has to come from your own resources or be gifted to you.I suspect it works similarly in your area.That said, there will be folks who will tell you ways to circumvent this requirement ... and it happens routinely, but in the end the lender could pull the plug on you if discovered ... or worse, the words mortgage fraud can come into play as you will likely attest that the downpayment comes from your own resources.

The title company that did the settlement offered a "gift deed" as a method to transfer ownership of the property, from my wife and I to the LLC.

Unfortunately, unless the money is gifted, it is not as simple as them just writing you a check.Passive investors receive at least 50% of the deal, and usually even higher based on your experience level.

@Robert SegerThe person giving the gift has to worry about the tax.

Here's something you don't see every day: https://www.seattletimes.com/business/real-estate/free-rent-in-seattle-no-catch-a-landlord-couples-faith-inspired-a-gift-for-tenants/

NAR/CAR ethics stipulate 'Seller is Agent' disclosure in writing on the MLS etc at time of listing because even if Seller is not the Listing Agent, licensed seller/owner may expect and/or receive compensation (ie, gift, referral fee, portion of listing agent's compensation, etc).Thus licensed seller is inherently not strictly limited to being a principal in the transaction, so would have had to disclose seller is licensed agent. 

Can I use someone else's money (that wasn't gifted or loaned to me) for my down payment on a bank loan?  

I offered just below that and she decided it was worth much less and is giving me a deal if not a gift, I am shooting more toward a deal since I know gifting could hurt either of us with the current taxes and I also planned to buy under my LLC and keep separate from my personal belongings. 

This person would be the primary one paying the mortgage and managing the property.Different Mortgage Loan scenariosApplying for loan soloApplicant 1 aloneThis applicant's credit is good enough that they would undoubtedly qualify for the best rates, but since they do not have a lot of cash on hand for a down payment they would need to either cash out some stocks or get a gift from Applicant 2.My understanding is that either option would lead to tax consequences.