  This article explores new physically viable wormhole solutions within the
framework of f(R,Lm) gravity theory, incorporating noncommutative backgrounds
and conformal symmetries. The study investigates the impact of model parameters
on the existence and properties of wormholes. The derived shape function is
found to obey all the required criteria. Specific attention is given to
traceless wormholes with Gaussian and Lorentzian distributions, investigating
the behavior of the shape functions and energy conditions. In both cases, the
presence of exotic fluid is confirmed.
