There are two issues here, and the first is arguably a bug that can be fixed.
The first issue is that you are specifying a 2D coordinate, with unspecified distance from the origin. Astropy raises the error you see when the transformation of a 2D coordinate includes a shift in origin, since handling such a shift is undefined. The transformation from LSRK to ICRS doesn’t actually include a shift in origin, but it does include a velocity shift, and the bug in Astropy is that the presence of the velocity shift is enough to trigger the above error, because the code doesn’t looking deep to check if the origin shift is actually nonzero. I encourage you to report this bug on Astropy’s GitHub, and it should be straightforward to fix.
In the meantime, you can easily work around this bug by specifying a distance, any distance, when instantiating your SkyCoord, e.g.:
mysource = SkyCoord('04h21m59.43s +19d32m06.4', distance=1*u.kpc,
frame=LSRK, radial_velocity=25* u.km / u.s)
After you address the first issue, the second issue is that you are specifying only a radial velocity, with unspecified proper motion. Astropy cannot apply the velocity shift between LSRK and ICRS without knowing what the proper-motion values are. If you intend them to be zero, you still need to specify them explicitly, e.g.:
mysource = SkyCoord('04h21m59.43s +19d32m06.4', distance=1*u.kpc,
frame=LSRK, radial_velocity=25* u.km / u.s,
pm_ra_cosdec=0*u.mas/u.yr, pm_dec=0*u.mas/u.yr)
Hope that helps!