There is a lien in place, customer wants want to give me partial payment, if I accept will that forfeit the lien since the amount now being owed to me is less than the amount stated on the lien?
You can still accept partial payment without giving up the leverage of your lien claim, as long as you don't execute a final, unconditional waiver for the full amount.
Florida lien laws do not contemplate nor technically require anything be done with a lien after partial payment has been made; such as a 'partial release' available in some other states. However, I'm sure the customer will likely want some sort of reassurance in exchange for payment. One option here would be to provide a partial, conditional waiver in exchange for partial payment. If the claim has to be enforced down the line, that waiver can be introduced in court to reduce the amount of the claim. Another option would be to file an amendment to the claim, but these are typically only available within the initial lien filing deadline.