Hi BillLake! Welcome, we're glad you found us!
There are a few lined pond owners, but liners are normally only used if you can't get or don't have good clay available. Worthwhile liners are made of rubber to pond size and are a minimum of 40 mil thick.
The cost of a liner is pretty high and is usually more to install than reworking your dam would cost. Plus it is unlikely you could just line your dam successfully...the water would just run under the liner if you have a leak already.
If you have good clay available at your pond site, a core trench is not absolutely required. You can line the water side face of the dam and the main pool area with about a 1 foot thick layer of well COMPACTED clay in 6 inch lifts, per 7 feet of depth....Use a 2 foot minimum thickness on the dam face and bottom though. The cost of this, including re-stocking, will often be far less than the price of a liner alone.
You may want to contact your county NRCS agent at your USDA office. Most are great people and the service is free. They can often give you some invaluable help. Asked quietly, most will suggest qualified builders (My NRCS agent even supervised the 58 hours worth of repairs on my pond)