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This work is an extension of our previous work [1] where we exploitedholography to compute the complexity characteristics of Little String Theory(LST), a nonlocal, nongravitational field theory which flows to a local 2d CFTin the IR under RG via an integrable irrelevant (TT) deformation. Here we lookat the more general LST obtained by UV deforming the 2d CFT by incorporatingLorentz violating irrelevant JT and TJ deformations on top of TT deformation,in an effort to capture the novel signatures of Lorentz violation (on top ofnonlocality) on quantum complexity. In anticipation of the fact that the dualfield theory is Lorentz violating, we compute the volume complexity in twodifferent Lorentz frames and the comparison is drawn between the results. Itturns out that for this system the nonlocality and Lorentz violation effectsare inextricably intertwined in the UV divergence structure of the quantumcomplexity. The coefficients of the divergences carry the signature of Lorentzboost violation. We also compute the subregion complexity which displays a(Hagedorn) phase transition with the transition point being the same as thatfor the phase transition of entanglement entropy [2]. These new results areconsistent with our previous work [1]. Null warped AdS3 is treated as aninteresting special case.

Holographic Complexity of LST and Single Trace $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$ deformations