  The magnetic, thermodynamic, and pyroelectric properties of LiFeP$_2$O$_7$
single crystals are investigated with emphasis on the magnetoelectric
interaction of the electrical polarization with the magnetic order parameter.
The magnetic order below T$_N\simeq$ 27 K is found to be a canted
antiferromagnet with a weak ferromagnetic component along the $b-$axis. A sharp
peak of the pyroelectric current at T$_N$ proves the strong internal
magnetoelectric interaction resulting in a sizable polarization decrease at the
onset of magnetic order. The magnetoelectric effect in external magnetic fields
combines a linear and a quadratic field dependence below T$_N$. Thermal
expansion data show a large uniaxial magnetoelastic response and prove the
existence of strong spin lattice coupling. LiFeP$_2$O$_7$ is a polar compound
with a strong interaction of the magnetic order parameter with the electric
polarization and the lattice.
