"Some" discharge if you use water based lubricant is normal, as well as "stickiness" of the removed lubricant out of the female dogs vagina. Wouldn't be different if you ejaculate inside of her, most will get flushed out by movements or peeing and she'll usually lick herself clean (which is not as easy with lubricant, that's why it can still be a bit sticky).
But this doesn't last days, more like a few hours, can as well get cleaned easily with a dampened soft cotton cloth. Quite a big amount will get ejected and removed by going on a pee walk a while after copulation / activities.
As well depends on amount applied (too much is never good, as it will either need to get flushed out / ejected or partly absorbed and transported through the body - as example the water that is in it).
But this harmless short-term removal out of the body has no relation to a false pregnancy.
As such, if you got a false pregnancy like in your case verified through the veterinary, that's a whole different story and the symptoms are possible over a longer time.