Output of marginally stable systems
An ideal LC circuit has no resistance, and hence no resisitive loss mechanism. Therefore if it starts to oscillate (due to, for example, a non-zero initial voltage or current stored in the L or C), then it will oscillate indefinetely on its own, yielding a situation as described in your question.
Zero input response of a linear system is the response under no input excitation but due to non-zero initial conditions.
Note the distinction between the terms linear time-invariant (LTI) and the broader term linear alone. The discussion in the Lathi's book is about linear systems in the more general sense.
Note also that a linear (but not necessarily LTI) system can have non-zero initial conditions, and hence zero-input response; but a strictly LTI system cannot have non-zero initial conditions, because one property of LTI systems is the initial rest property. Hence zero-input response of LTI systems is zero by definition.
So by definition a system with zero-input response cannot be LTI, but it can be linear nevertheless...