Yes you can. There are many lenders (including my bank) that allows you to use your paid off lot as a down payment. We give a construction loan that is changed to a regular mortgage after the CofO is in place.
Your best bet for this type of loan is to contact a local credit union. You would be doing a construction perm style loan. The terms are not always the best but you can refinance out of the loan once the perm loan is issued. Any other questions please feel free to contact me.
You can contact a lender that specializes in new construction loans. If you have a recent appraisal that will be helpful in determining the amount of equity you have. Do you already have a builder in mind? Where is your lot located?