We investigated spin-lattice coupling in orthorhombic pseudobrookite ${\mathrm{FeTi}}_{2}{\mathrm{O}}_{5}$ single crystal with highly ordered $\mathrm{F}{\mathrm{e}}^{2+}$/$\mathrm{T}{\mathrm{i}}^{4+}$ occupation, which consists of quasi-one-dimensional (1D) $S=2$ chains running along the $a$ axis. Both the magnetization and specific heat measurements confirm that the antiferromagnetic phase transition of ${\mathrm{FeTi}}_{2}{\mathrm{O}}_{5}$ occurs at ${T}_{N}=42\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The structural distortions were also observed around ${T}_{N}$ in the thermal expansion $\mathrm{\ensuremath{\Delta}}L/L(T)$ data. Moreover, the magnetic field was found to strongly affect the thermal expansion both along chains and in the perpendicular direction clearly signaling a substantial magnetoelastic coupling, which was recently proposed to be the origin of a rare spin Jahn-Teller effect, when frustration is lifted via additional lattice distortions. Experimentally observed change in the thermal conductivity slope around ${T}_{N}$ is usually associated with the orbital ordering, but density functional theory (DFT)+$U$ calculations do not detect modification of the orbital structure across the transition. However, the first-principles calculation results confirm that ${\mathrm{FeTi}}_{2}{\mathrm{O}}_{5}$ is a quasi-1D magnet with a ratio of frustrating interchain to intrachain exchanges ${J}^{\ensuremath{'}}/J=0.03$ and a substantial single-ion anisotropy $(A=4\phantom{\rule{0.16em}{0ex}}\mathrm{K})$ of easy-axis type making this material interesting for studying quantum criticality in transverse magnetic fields.