  We study the kinematics of luminous blue variables (LBVs) in the Large
Magellanic Cloud (LMC). Using high-resolution spectra, we measure the systemic
radial velocities for a sample of 16 LBVs and LBV candidates. In order to
measure the net motion of LBVs compared to their local environments, we
subtract the projected line-of-sight velocity at the same location derived from
the rotation curve model of the LMC. Using nebular and wind emission lines, we
infer a velocity dispersion for LBVs of $40.0^{+9.9}_{-6.6}$ km s$^{-1}$. To
put LBVs in context with other evolved massive stars, we compare this to red
supergiants (RSGs) in the LMC, which have a significantly smaller velocity
dispersion of $16.5^{+0.4}_{-0.6}$ km s$^{-1}$. Moreover, 33% of LBVs have
radial velocities of more than 25 km s$^{-1}$, while only 9% of RSG have such
high velocities. This suggests that LBVs include more runaways than the
population of stars that evolves to become RSGs, indicating that LBVs are
preferentially kicked by a companion's supernova explosion as compared to other
evolved massive stars. Our investigation reveals other interesting clues about
LBVs in the LMC as well. We find that radial velocities and widths of emission
lines for each target remain constant over several epochs, whereas measured
absorption lines exhibit highly variable radial velocities for R110, R81, S
Dor, Sk-69$^\circ$142a, and Sk-69$^\circ$279. These five LBVs probably have a
binary companion. Additionally, we find that Sk-69$^\circ$142a experienced its
second outburst in 2019 September, shifting its status from candidate to
confirmed LBV.
