Driven by recent anomalies in flavour-changing neutral current (FCNC) transitions in \( b \rightarrow s \ell ^+ \ell ^- \) decays, we investigate lepton flavour violating (LFV) decays via \( b \rightarrow ~\hbox {s} \ell _1 \ell _2 \) transitions ( \( \ell _1 \ne \ell _2 \) ). While absent in the Standard Model (SM), these transitions naturally emerge in SM extensions, such as models with vector-like fermions or an extra \( Z' \) boson. Using a model-independent approach, we analyze LFV decay channels \( B \rightarrow K^* \ell _1 \ell _2 \) , \( B \rightarrow \phi \ell _1 \ell _2 \) , and \( B \rightarrow K_2^* \ell _1 \ell _2 \) . We derive angular decay distributions, set bounds on branching ratios, and examine the leptonic forward-backward asymmetry, providing insights into potential new physics.