I've used several lubes to dilute like this, but not Lee's. because of that I don't know how helpful this will be in your case.
I use "Yellow Heet" gas line dryer for the alcohol. Its pre-mixed, comes in small quantities & dissolves, Hornady, RCBS & Pacific lubes very easily. I put one full bottle of the lube in a full bottle of "Heet" & shake vigorously. To stop evaporation I store it in 1 Pt nalagene bottles with a screw top. I've stored mixed alcohol-based lubes in quantity for a couple of years this way.
When I want to lube cases I just shake it up to make an even mix, decant a couple of ounces into a small pump spray bottle I kept from a pump spray cleaner.
If you mix is sperating then you can probably just re-mix it with a good shake right before spraying.
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Allan Quatermain: “Automatic rifles. Who in God's name has automatic rifles”?
Elderly Hunter: “That's dashed unsporting. Probably Belgium.”