Spin fluctuations were studied over a wide momentum ($hbar Q$) and energy ($E$) space in the frustrated $d$-electron heavy-fermion metal LiV$_2$O$_4$ by time-of-flight inelastic neutron scattering. We observed the overall $Q$$-$$E$ evolutions near the characteristic $Q=0.6$ {AA}$^{-1}$ peak and found another weak broad magnetic peak around 2.4 {AA}$^{-1}$. The data are described by a simple response function, a highly itinerant magnetic form factor, and antiferromagnetic short-range spatial correlations, indicating that heavy-fermion formation is attributable to spin-orbit fluctuations with orbital hybridization.