Hi Gielt,
The flash point for lubricating oil is around 225°C and for olive oil around 210°C so I wouldn't think that there is much of a serious problem there. There is however a problem when vegetable oils are used with cotton cloths. If saturated cloths are kept in bulk, say a waste bin, the heat generated by reactions between the oil and cotton is trapped in the container and can increase until combustion takes place spontaneously. I don't think that it is a problem with mineral oils.
Alcohol on the other hand has a flash point around 14°C hence the admonition not to smoke or strike a match when using but it is unlikely to combust otherwise but yes, a fireblanket within easy reach is the very minimum precaution.
I have had a workshop fire (electrical fault) and it is not a pleasant experience.
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In full blaze
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Aftermath. Both cars scrap as well.
Fortunately I had good, but expensive insurance which covered rebuilding and all contents luckily, but I am now extremely, perhaps overly cautious. Picture taken by a neighbour from his garden.
TerryD