Neutron stars are extremely relativistic objects which abound in our universe and yet are poorly understood, due to the high uncertainty on how matter behaves in the extreme conditions which prevail in the stellar core. It has recently been pointed out that the moment of inertia I, the Love number lambda, and the spin-induced quadrupole moment Q of an isolated neutron star, are related through functions which are practically independent of the equation of state. These surprising universal I - lambda - Q relations pave the way for a better understanding of neutron stars, most notably via gravitational-wave emission. Gravitational-wave observations will probe highly dynamical binaries and it is important to understand whether the universality of the I - lambda - Q relations survives strong-field and finite-size effects. We apply a post-Newtonian-affine approach to model tidal deformations in compact binaries and show that the I - lambda relation depends on the inspiral frequency, but is insensitive to the equation of state. We provide a fit for the universal relation, which is valid up to a gravitational wave frequency of similar to 900 Hz and accurate to within a few percent. Our results strengthen the universality of I - lambda - Q relations, and are relevant for gravitational-wave observations with advanced ground-based interferometers. We also discuss the possibility of using the Love-compactness relation to measure the neutron-star radius with an uncertainty less than or similar to 10% from gravitational-wave observations.