Check the connections at the battery, they could be loose or corroded. If corroded then loosen the nuts & remove the terminals, then pour boiling water over the terminals and poles to melt off the corrosion. Perhaps remove the battery & recharge it.
+1 on the battery terminal posts...
If you're seeing lights (Red oil pressure and battery) illuminated prior to cracking that's normal.. IF, when you crank, there is a 'click' from the engine and all the lights extinguish (including your dome/interior light) then you have one of three problems:
1 - Car Battery issues- dead cells internally - need new battery.
2- Dirty corroded battery terminal posts (or dirty corroded battery connectors/clamps) - Need to clean.
3 - Broken/Jammed/Stuck started motor - break out the spanners.
My money would be option '2'.. the corroded (fur) surfaces between the battery posts and the crimps/clamps. I remember our 156 used to have savage fur growing on the negative terminal.. I don't now if it was due to the metal alloy in the negative crimp or the chemical make up of the last battery in there... but I would have to clean and de-fur 2 to 3 times a year.
There is a tool for cleaning the posts.. see picture of 'silver tool' included here. I think they were a few euro in Halfords a few years back.. if used gently it'll last >10 years. It comes in two parts.. the piece you see below slides over the battery post and 'sands down' the fur.. the 2nd piece has this internal wire brush from cleaning the inside surface of the battery leads/crimp/clamps.
Also just included a typical picture of battery 'fur' so I don't sound mad...
BTW. an O2 (lamba) fail or error shouldn't stop a car from cranking/starting.
The missing coolant needs to be investigated asap too. Hopefully it's a cracked pipe or leaky radiator... I hope it's not a gasket issue. Does the engine oil (on dip stick) look brown/black? Or is there mayonnaise in there?
Best of luck with car, keep us posted!