The LOD plots at IERS start in 1992:

but I think they have measurements since around 1973/1974:

I doubt that tidal observations are so precise that you may reconstruct the LOD in milliseconds.
It seems that there are some historical records on lunar occlusions or maybe other celestial observations, which are eventually combined with reconstructions of the earth magnetic field, but this seems not easy at least here

"The evolution of the core-surface flow over the last
seven thousands years"
by I. Wardinski and M. Korte from 2008

it is written:

>Recently, Dumberry and Bloxham [2006] sought
time–dependent azimuthal flows from an archeomagnetic
field model and compared the variations in the core angular
momentum computed from these flow solutions to the
observed variations deduced from records of historical solar
and lunar eclipses [Stephenson and Morrison, 1995]. Their
study shows that assumptions made to derive core angular
momentum changes on a decadal timescale prove to be
invalid for millennia.

Where I sofar didnt manage to find out at what place in history they started to count in seconds and then in milliseconds.