Hello Tony,
I'm not an attorney so can't answer specific legal advice but I can say what I've done myself and some of our users at EasyTrustMaker have done this--
Living Trusts & Due On Sale Clause
If this is a primary residence, the "Garn-St. Germain Act" protects homeowners from the "due on sale" clause.
As far as "due on sale" clause for non-primary properties, you can speak with the lender if you'd like but I have't heard of it being an issue.
BE SURE TO ALERT HOME INSURANCE OF THE NEW "OWNER" (your living trust which you control / manage).
I have yet to hear of a bank actually enforcing this as long as you pay the mortgage on time.
Although, technically they could. There are many ways the bank can try to due on sale a property, but if you are paying the mortgage, in our current economic state, they probably wouldn't want to (eg: It costs $$$ to acquire new loans, by calling yours due they then need to reinvest the money elsewhere).
LLC
I can't recommend a course of action for your LLC <> Living Trust, but I have heard of people making the Living Trust a beneficiary (eg: if/when something happens to you, the living trust takes over, so then the named beneficiaries in the living trust and terms are referenced). There are many other methods to go about this... Eg: The living trust is a member in the LLC and both spouses have a "joint revocable living trust", etc...
You'll want to explore tax implications if you're moving property to an LLC.
*Note: I am not an attorney, financial specialist, tax advisor or law office. This is informational only and not a recommendation on what to do for your personal situation.