How do lenders count equity in land you already own?

If land is being used toward a construction loan’s equity requirement, how does the lender usually decide what value to count? Is it based on an appraisal, the price paid, or another figure, and when does that valuation need to be completed?

I’d also like to understand how an existing mortgage or other lien changes the calculation. If the land’s eligible equity falls short of the requirement, can cash make up the difference, or might the lender require cash regardless?