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Would try cutting fluid if I had some- will give chain lube a go.
Chain lube will be fine, but if you're going to bodge it use something cheaper.
I'm pretty sure mine is 50:50 water and fresh* engine oil. You just need something to help cool and lubricate. Water is great for both those things but evaporates and runs all over the place hence the oil. You could also use sunflower oil and water if you don't have engine oil - although if you do engine oil would be better as it's designed to lubricate and won't go sticky.
*although it's obvs not fresh anymore.
Sounds like the bit is blunt now. Maybe use cutting oil in future.