You'll need to add a root barrier between the tree roots and the pond. That means digging out between the two. Beech have shallow roots, so a 2 foot root barrier may do the trick, but a 3' one would be a safer bet. Doing a pruning type install on a tree that close to the pond will likely shock it very badly, so this means moving your pond out quite a long way if you truly want to save the tree (I'm not sure 2 feet would be enough). Might be better to just let it go and take a "wait and see" approach. The roots might never penetrate the liner. I doubt it would happen in a fantastic rupture type event, where all the water drains out overnight. Just so long as you check the water level daily so you catch any leaks quickly, I don't think it will result in that nightmare scenario happening. Especially since the roots will slowly push the bottom up where they are, making a deeper end on the side away from the tree where fish can go if a leak ever occurs.
For tree barriers, you need a solid type, not a simple flexible "bamboo barrier". It's going to have to be rigid. DeepRoot makes the best root barriers, see
https://www.deeproot.com/products/root-barrier.html and
https://www.amazon.com/DeepRoot-UB-24-2AMZ-Barrier-Black/dp/B01CXQGFYI/ref=sxbs_sxwds-stvp. You will need to connect as many as you need to make a wide enough barrier to protect that entire side of the pond. This will force the roots to either go deeper, or grow more away from the pond, under the fence in the background. Depending on what's on the other side of that fence, that might not be preferable.