How to lock a property

For simple position animation with no parent layer all you have to do is enter the desired value of the Y position in a simple array. If you wanted the Y value to always be 300 the expression would look like this:

[value[0], 300];

 If the layer is the child of another layer (Parented), then you subtract the toComp(anchorPoint) of the anchor point from your desired Y position like this:

tPos = parent.toComp(anchorPoint);
[value[0], 300 - tPos[1]]

 That will make the X position follow the Null and hold the Y position at 300. 

You can throw in an if/else statement that looks for a parent layer like this:

if(thisLayer.hasParent){
	tPos = parent.toComp(anchorPoint);
	[value[0], 300 - tPos[1]];
}
else{
	[value[0], 300]
}

That way you only have to write one expression.  You could also tie the Y position to an expression control slider.

If those two solutions don't solve your problem then we need a screenshot showing exactly what you need and a detailed workflow and design description.