Hi, Ion Swamp
By “lake” do you mean the one that rolls and drills forward (and also corresponds to the clouds), or do you mean the one that is like the thunder palm, only angled downward (the water palm)?
The way I took your term was the one that rolls and drills forward. If that is the case, I would say no, you should not do that, but for different reasons. And those reasons have to do with the Lake palm.
The left Lake/Cloud palm to a left punch will land his punch right on your mouth, and you will not have the opportunity to do anything else. If you are using this one, you might want to roll the palm onto the inside of his arm, then turn it into a Water palm to pull his arm down and to your left, and then you can get in to use the Thunder palm. If you are going to hit him in the back of the head with it, you should strike to the soft spots just below the skull on either side of the spine, which is Gallbladder 20. He will drop right to the ground. However, I think Fire palm would be more suited to soething like this, though Thunder is perfectly acceptable if you have conditioned the back of your hand and wrist to take hitting the bone (just in case you miss).
On the other hand, if you are talking about the Water palm, using it to block a low left punch, take it over to your left, and use Thunder to the back of the head, that’s perfectly workable, though I would still use Fire for the final strike, myself.
Of course, you could always use a left Thunder to block a left punch to your face at the inside elbow, then drive it down and pull it to your left, using Water, and then use Thunder or Fire to strike the head.
Or you could use a left Thunder to block on the outside of his arm, then use a right Fire to the elbow, or the temple, or drive it upward into the GB20 spot.
I like to strike with the back of the Thunder palm myself. My main art is Taiji, of course, and we use P’eng (the Thunder palm) to strike a lot, as well as block and redirect. In fact, one of the Yang family manuals talks about being struck with P’eng. So if you want to strike with the back of the Thunder palm, by all means do so, there’s nothing really wrong with it as long as you don’t injure your hand by striking the wrong places.
If you do strike with it, start with the palm flexed a bit the other way, and pop it into the Thunder shape as you thrust it into your target. This will make your strike more powerful.
“I put forth my power and he was broken.
I withdrew my power and he was ground into fine dust.”
-Aleister Crowley, The Vision and the Voice