Well, if the serial interface output is the only port you can access, the only chance is to see if the GPS module is one of the "Frequency and Time Sync" modules from UBLOX. Those are able to discipline a LO by themselves and if you enable the correct messages, you have enough information for Lady Heather. So, the job is then to modify LH to understand this data.
If the GPS module cannot supply the disciplining data and no other interface is available, your journey ends there, if you don't want to use extra hardware.
What you could do is order a TAPR TICC (it's about $250), which LH supports, and feed it the 1PPS signal from the GPS module and the 10MHz from the LO and see what you get there. No idea if LH can work both with a GPS and the TAPR TICC but it's worth a shot.