Again, if you want to lock something then define the value in an expression. Almost every parameter is lockable. If you can add an expression to a property you can probably lock it.
As far as applying LUTs through Lumetri then some, not all, but some of those parameters are lockable. You cannot generate a curve with expressions or pick a preset and lock it.
A general color correction that will apply your carefully designed look to footage without changes cannot be successfully created because every shot is different, the color balance is different, the average gamma is different. Color correction can generally be applied to an entire film but every scene needs its own color fine-tuning. I'm currently color grading a short film and one key scene was carefully lit and shot. Every aspect of the exposure was discussed with the camera operator, the DP. Every bit of the lighting was locked down before filming began on this indoor location. The lenses were Zeiss primes are perfectly color matched, the ISO setting was the same, the T-Stop (f-stop) was always F4 and when it came to the final color grading of the scene everything shot from stage right had a slight yellow shift in the highlights because of reflected light coming from the left. None of those yellow highlights existed in the shots from stage left. A general LUT (color grade) was applied through with an adjustment layer to the 26 shots that made up the scene and an additional LUT was applied to all of the 9 shots that came from Camera Right where we just pulled down the yellow saturation in the highlights. Only 2 of the 9 shots used exactly the same settings. Leaving the yellow highlights alone was not an option.
The point of the story, there is no one color correction that will work for every scene in every film and locking your look is not going to guarantee that any two shots will look the same.
My instructions for saving an animation preset work without keyframes. All modified properties of an effect are saved including any custom names you have given to the effects unless you select a specific property in the effect. If you have applied 20 effects to a layer and modified most of the properties in all 20 effects and renamed 18 of the 20, just selecting Effects in the timeline will preserve everything that has been modified. If you select one property or all properties in all of the effects then the custom names will not be saved and if you happened to miss one effect that you modified, like a color for a Tint effect, then that property will not be included in the animation preset. I hope that is clear. It's really easy to do right. It is more difficult, and unfortunately more common to do it wrong.
I hope this answers some of your questions. The short answer to the original post is "save an animation preset using the proper technique and everything is preserved. Many, probably most properties can be locked using an expression." The question you should probably be asking yourself is saving a completely locked color grading preset a good idea because every shot responds a little differently to color grading.