Hi:
I would consult a few manufacturers, regarding anchor trench need. Maybe Gundle and others. Do a Google search, if you need manufacturers names. They sell it and would surely know what applications do and do not need a trench. I am sure they have data on soil interface friction. Also, there are products with one side of the HDPE has a rougher texture to reduce slippage. If the lysimeter is a relatively small balanced structure, and the slopes not too steep, you may not have a problem.
Scott