Generally speaking, you may lock an interest rate once.
When you lock a rate, you are asking the lender to make a commitment to deliver your loan upon closing into a specific investment pool with a specific yield on the investment. Lenders will not allow you to re-lock for a lower rate (see exception below) in the same way that lenders do not increase your rate after locking in a rising rate environment. The point of a lock is to freeze the rate for you, the lender, and the future investor during the underwriting process.
Many lenders offer a "float down" options, which allows you to re-lock at a lower rate should rates fall during your lock period. The float down must be specified prior to locking; it may come with a fee; and in general it can be exercised once. Float-down options are typically offered on construction-to-permanent loans since C-to-P lock periods often extend up to a year.
A decision to pay for a float down option prior to locking or to execerise a float down option after locking depends on the fee and the length of time you expect to own your home. In most situations, purchasing a float down option is a wise idea. If you expect to own (or retain the mortgage) for a short period, the fee may exceed the payment savings. Your mortgage sales rep can work out the figures for you both ways to assist in making a decision.