Congruent lithium niobate (LN) doped with rare-earth ions is a promising material for integrated optic applications combining the properties straightforwardly associated to the dopant with lasing and good electro-optic (EO) properties. By direct technique based on optical arrangement of Mach- Zehnder interferometer associated to the Modulation Depth Method using He- Ne laser with the beam at the wavelength of 633 nm and at room temperature, we have experimentally determined the figure of merit F = n3reff, (n is the refractive index and reff, the effective EO coefficient) and finally calculated the EO coefficients reff of the third-column of the unclamped electro-optic tensor of singly (Yb3+, Ho3+, Tm3+) and doubly (Er3+-Yb3+) doped LN crystals. It is found that in all the studied opto-geometric configurations, the unclamped figure of merit and consequently the corresponding electro-optic coefficients of the crystals under study remain quasi-constant in the considered dopant concentration range (0-1mol%). As the figure of merit, F qualifies crystals for electro-optic modulation and laser applications, all reported results confirm that the LN doped amd/or co-doped with rare-earth elements are very promising versatile candidates for several multifunctional nonlinear devices in optoelectronic and laser applications.