I've also had problems with the Lee bottom pour feature in both of my furnaces: dripping and poor flow to be specific. I tried all the remedies already mentioned, but ultimately plugged the spouts and used a ladle for casting. The Ideal/Lyman egg shaped one works well, but look around for one which may suit you better.
Btw, sometimes Lee furnaces need their thermostats adjusted so they put out enough heat to melt lead. It's a simple enough job*, but it requires unscrewing the top plate, i.e., the one with the temp. control knob.
*Clean the points of the bimetallic thermostat first, then gently bend the lower one down a bit.