Hi Julia,
The child support order is typically issued by the department of revenue for the state of Florida. In this case, the lien will likely survive. There may bne a case that it will not survive if it is not attached to the specfic property in question.
For safety I would assume it survives.
Reference Florida statutes
FL 55.10
FL 197.552
FL 197.122
EDIT: For clarification on the timeframe, the state can renew the order and extend it past 20 years. There is a 20 year statute of limitation on a DOR order but they may have extended.