Mm-sized LiMn\(_{1-x}\)Fe\(_x\)PO\(_4\) single crystals with \(0\leq x \leq 1\) were grown by means of the traveling floating-zone technique at elevated Argon pressure of 30~bar. For the various doping levels, the growth process was optimized with respect to the composition-dependant effective light absorption and transparency of the materials. A convex crystal/melt interface, determined by the angle of incident light, was identified to be particularly crucial for a successful growth. The resulting large single crystalline grains are stoichiometric. Structure refinement shows that lattice parameters as well as the atomic positions and bond lengths linearly depend on the Mn:Fe-ratio. Oriented cuboidal samples with several mm\(^3\) of volume were used for magnetic studies which imply an antiferromagnetic ground state for all compositions. The N\'eel-temperature changes from \(T_N\) = 32.5(5) K in LiMnPO\(_4\) to 49.5(5) K in LiFePO\(_4\) while the easy magnetic axis in the ordered phase flips from the crystallographic \(a\)- to the \(b\)-axis upon Fe-doping of \(x<0.2\).