Catching up a lag

Solution 1:

You could say, "The server is now up-to-date."

extending up to the present time : including the latest information (M-W)

This is similar to Ramrod's comment, but a bit more commmonly used, IMO.

The sever was lagging for a week but now it is up-to-date with the master.

Solution 2:

Having worked in (medical) IT for many years, we always just say "the lag has been corrected" or "is gone" ;) no, there is not any particular word to use though something denoting synchronicity is close... it's not really appropriate to the use with servers and databases in this regard.