How can we place a valuation on a start-up LLC per the conditions stated below?

We are forming a new LLC with virtually no monetary or physical assets in the company except for a patent. In case of the untimely demise of one of the members we would like to place a valuation on the LLC for the benefit of the heirs. At one point there was a preliminary offer to buy the patent for $5M. Can we arbitrarily use this for the initial valuation, or can we use the anticipated revenue of the LLC based on the business plan as the basis?

Yes. You and your partners can choose any valuation you like. Either the preliminary offer of the patent, or anticipated revenue is fine for the purpose. The patent offer is probably more defensible.

When it be come relevant to someone outside of the members of the LLC -- like an investor, your preconceived value will be worth only the degree to which the other parties agree or support it.

Be sure not to forget the other issues associated with an untimely demise of one of the members. Among those are the tax implications of a high value on the benefits, the need for a will, and the opportunity associated with "key person" insurance on the LLC members.