Can I assume system is LTI when given by DTFT of impulse response
A 1D LTI system is completely characterized by the function $h(t)=T\{\delta(t)\}$ which is denoted as the impulse response of the system. Given an LTI system with impulse response $h(t)$ you can then find its frequency response as $H(j\omega)=\mathcal{F}\{h(t)\}$ where $\mathcal{F}$ stands for continuous time Fourier transform.

When a system is not LTI but, for example, linear time-varying, then it's characterization is possible with the 2D function $h(t,\tau)=T\{\delta(t-\tau)\}$ which is the response of the system to an impulse applied at time $t=\tau$ 

When such is the case, the Fourier transform can be aplied in the following sense, treating $\tau$ as fixed (or as a parameter) the Fourier transform $\mathcal{F}\{h(t)_{\tau}\} = H_{\tau}(j\omega)$. So in effect you have to consider 1D CTFT for each $\tau$. Whether this is a useful representation or not, or there are other more useful representations for such systems, requires an indepth analysis of time-varying systems.