I've got a 2001 Disco II and it has started having issues starting in cold weather. If it’s cold out, it won’t even try and turn over. All of the electronics work (lights, radio, heat/air), it just won’t do anything when you turn the key. This only happens in cold weather, absolutely no issues starting when it’s warm.
Have you checked battery voltage before cranking as well during cranking plus checked what the current draw the starter is pulling during cranking?
A starter even if it turns over the engine to what seems normal cranking speed or most the time below can be drawing an excessive amount of current, adding to this any battery saturated overnight at your low temps it will not produce the current output demanded of it. Back to the excessive starter current drain plus lower battery output under starter load the voltage drop to the ignition system can now be compromized to a point of a weak or no spark hence no starting condition. Add to this the drag internally the oil which you should be using, a multiweight weight to the temps your LR will be operating at, thinner in the winter, thicker in the summer.
You have a healthy battery able to produce the current demands at your low temps, this by meter checking with a digital voltage meter not guessing calling it good?
Every connection starting from the battery terminals to the starter and back to the engine block and battery, all connections clean and bright plus torqued down tight? On an added note even with clean connections each connection will read app 0.30 ohm per connection. If cleaned and a product called KOPR-SHEILD a conductiove anti-corrosion surface compound were applied, each connection joint resistance will of dropped down to 0.10 ohm each on average This adds up each joint making it a big deal when only working on a 12 volt system.
Your LR still have LR's Lucas single dribble (1980's design) fuel injectors? Bosch 4 hole injectors allowing finer fuel droplets or spray times four which all adds up to finer fuel particles which are also easier to ignite, 2000 era tech injector upgrade vs those Lucas injectors. This also an advantage in helping with starting in your cold climate conditions, better running overall including a slight mpg improvement as well cleaner if smog test exhaust reading numbers.
This brings up another topic, what's your fuel rail pressure in psi?
LR had a fixation running a 2.5 Bar pressure regulator which when new hovered at the minimum rail pressure readings. Not your year of LR but my 95 D1 the 3.0 Bar pressure regulator for a late 80's BMW a direct swap allowing proper pressure for the injectors now having a pronounced spray pattern vs the reduced flow, again better and finer fuel atomizaton of the fuel also easier to ignite. Isn't that what you want, a bang result?
Battery heating pad as well oil pan pad or a engine block heater installed? Your cold climate must be hell on cold start engine wear vs 50*F considered cold where I live during winter.
Your engine's screaming for a Pre-Oiler system at those low temps.
We (wifey) had gone through starters since 1-2000 new ownership the 95 D1 5 spd but able to bump start to get the wife home again 6-7+ different times over the years. The D1 was used for kids school hence a Soccor mom vehicle for several years being started several times daily. My findings, Lucas starters crap, Bosch starters crap after swapping them out as well rebuilding them. Plastic parts in the planitary system very cheaply made also have fallen apart. One starter rebuilder I kept as a close friend suggested a Nippon starter. That one Nippon starter has outlasted all the above starters combined period. I found an honest and unbiased by brand starter and alternator rebuilding shop. Must mention even down to the low 20's F, by the 3rd, 4th max cylinder over compression the engine is fired up and idling, no long cranking also a feature allowing starters to live a longer life. In normal 50 -60*F cold starts by the 2nd over compression everytime firing up.
I'll shut up now......~~=o&o>......