Lithium niobate crystals were grown in 3D through localized heating by femtosecond laser irradiation deep inside 35Li2O-35Nb2O5-30SiO2 glass. Laser scanning speed and power density were systematically varied to control the crystal growth process and determine the optimal conditions for the formation of single crystal lines. EBSD measurements showed that, in principle, single crystals can be grown to unlimited lengths using optimal parameters. We successfully tuned the parameters to a growth mode where nucleation and growth occur upon heating and ahead of the scanning laser focus. This growth mode eliminates the problem reported in previous works of non-uniform polycrystallinity because of a separate growth mode where crystallization occurs during cooling behind the scanning laser focus. To our knowledge, this is the first report of such a growth mode using a fs laser. The crystal cross-sections possessed a symmetric, smooth lattice misorientation with respect to the c-axis orientation in the center of the crystal. Calculations indicate the observed misorientation leads to a decrease in the refractive index of the crystal line from the center moving outwards, opening the possibility to produce within glass a graded refractive index single crystal (GRISC) optically active waveguide.