Since the physical properties of lithium borate glasses xLi2O-(1-x)B2O3 (0<x< 0.28) vary over a wide range with the composition, this binary system is particularly suitable for studying the relationship between vibrational anharmonicity and fragility. The density, the linear expansion coefficient, the longitudinal and transverse ultrasonic velocities and their respective temperature coefficients of the velocities are measured, from which the vibrational anharmonicity in lithium borate glasses is evaluated with the help of the Grneisen parameter at the Debye cut-off frequency and the Anderson-Grneisen parameter: these two parameters plotted vs. composition have the same characteristics with minima at x≈0.08. The fragility is evaluated from the temperature width of the glass transition; the fragility also shows a minimum at x≈0.08. The presence of minima at x≈0.08 is ascribable to the fact that the crosslinking density between six-membered rings in the glass reaches a maximum at this composition. We show that the anharmonic parameters strongly correlate with the fragility metrics.