The azimuthal correlation angle between the scattered lepton and the leading jet in deep inelastic $e^{\pm}p$ scattering at HERA has been studied using data collected with the ZEUS detector at a centre-of-mass energy of $\sqrt{s}= 318$ GeV corresponding to an integrated luminosity of 326 pb$^{-1}$. A measurement of jet cross sections in the laboratory frame was made in a fiducial region corresponding to photon virtuality $10 < Q^2 < 350$ GeV$^2$, inelasticity $0.04 < y < 0.7$, outgoing lepton energy $E_e>10$ GeV, lepton polar angle $140^\circ < \theta_e < 180^\circ$, jet transverse momentum $2.5~\text{GeV} < p_\text{T,jet} < 30~\text{GeV}$, and jet pseudorapidity $-1.5 < \eta_\text{jet} < 1.8$. Jets were reconstructed using the $k_{\text{T}}$ algorithm with the radius parameter $R=1$. The leading jet in an event is defined as the jet that carries the highest $p_\text{T,jet}$. Differential cross sections were measured as a function of the azimuthal correlation angle in various ranges of leading-jet transverse momentum, photon virtuality and jet multiplicity. Comparisons between the HERA data and perturbative calculations at $\mathcal{O}(\alpha_{s}^2)$ accuracy are presented, providing insights for future experiments, such as the U.S.-based Electron-Ion Collider.