You'll want to pressure wash the entire thing. if you start seeing cracks or if you take a hammer and just tap the concrete you'll hear a solid sound " a good thing" or you'll hear what sounds hollow ": not so great" cracks that you can feel with a fingernail "not so good"
i do suspect on the right side of the photo at the top that those rocks are hollow sounding and the mortar/ concrete has failed.
I love the supported rock, but unfortunately if you do need a liner it will have to go. ORRRRRR YOU MAYBE ABLE TO APPLY a new water proof coating like fiberglass or a polymer over the existing after some repairs.
in the same respect the person that built that free floating rock had to have a clue what they were doing so that is encouraging.