All of the pail pumps I have seen, including the pump I have but have never used, require the lid to come off. You could dump it in a five gallon bucket and use a standard pail pump? I buy the same brake cleaner from AutoZone and this is what I do: At one time I was buying BrakeClean in the gallon jugs so I saved one and use a siphon hose that I bought at Menards to transfer from the five gallon can to the one gallon jug about every other month, then use a funnel to pour it into the Sure Shot. When the last of the five gallon can goes into the one gallon jug, I know I have a little time but need to get me another five gallons sooner than later. I did try one of the drill pumps to transfer and it worked...once. The brake cleaner ate up everything inside the pump, leaving it as nothing more than dumpster filler.
On another note, even though I use the same cleaner, it isn't all that great. I keep a can or five of the good stuff on the shelf at all times.