Output of marginally stable systems In' b.p lathi's book of systems and signal it is written that
&quot;marginally stable systems have one important application in the oscillator, which is a system that generates a signal on its own without the application of an external input. Consequently the oscillator output is a zero input response &quot;
By this statement I have two problem:

if let's say oscillator system is a simple L-C circuit then how can it produce output without input and if it does produce then isn't it a violation of linearity?

and if initial conditions are zero then how can L-C  circuits have zero input response? And then in that case how does it generates signal without initial conditions?
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...