The Lagonda 2.6 & 3ltr Models have largely the same issues as the DB2 to MkII Models,
The cooling system on a these engines is a fairly simple system that works very well if kept in good condition, it has a capacity of 24 UK Pints or 13.63 ltrs for Lagonda 2.6 & 3 lts models (from an original Service Manual)
The radiator is a brass & copper one with the header tank on the top of the radiator, the system is pressurised to 4lbs,
The water pump is driven by a shaft from the timing gear & is at 1/2 engine speed. The only faults that normally occur with the water pump are:
Wear on the thrust washer on the impellor, this is an easily replaceable part that pulls off & presses onto the impellor, it needs to fitted with a new gland seal.
If the gland seal behind the impellor leaks there is a dribble from the 'weep hole' behind the ignition coil (on the same side as the carbs) on the timing case, if the 'weep hole' is blocked up there is a good chance that the coolant will then leak into the lubrication system with similar symptoms as a leaking head gasket.
If oil leaks from the weep hole, remove the cover, impellor, gland seal & flinger (if fitted) then the oil seal can be prised out, if fitting a new oil seal (with the lip facing the oil side to keep the oil in the timing cover) doesn't work, the timing cover will need to come off then most of the timing gear & a new intermediate shaft fitted, possibly new chains, tensioner bushes, certainly new crank oil seal, this may mean you will need the help of a specialist but it is a job that a competent person can carry out.
The thermostat is in the top hose on 2.6 & some 3 ltr models, its in the themostat housing on later 3ltr models, if later stat is removed or a new one fitted which is a waxstat disc from some suppliers (without the complicated bypass part on the back of the stat) 80% of the coolant flow never gets to the radiator, it just keeps circulating round the engine getting hotter & hotter.