Well actually, there is a much cleaner and more methodical appraoch to this, and it even gives you control of the eyelid also.
Firstly, create a an eyeball. Then duplicate it, and enlarge it. Now you can chop up the larger one, that forms the eyelid and even extrud it or whatever to give it some depth. Now, both spheres should still have the same pivot point (centred). ...
Next, creata a locator, snap it the centre of the eye, NOT constrain. Enlarge the locator so that it is bigger than the eye...i.e. it is easy to select.
Now setup the aim constraint before you apply a lattice...create a locator, select the locator, then the eyeball, constraints>aim. If it doesn't just work when it is applied...i.e. the eyeball turns round and the area of the pupil is not aiming at the constraint, all you need to do is apply a -1 or a 1 figure to one of the aim constraint's 3 axis in the option box when you make the constraint...i.e. it is reorienting the eye to aim correctly by correcting the 90 degree offset of the object's normal.
Next, group the eyeball and the eyelid together and very important...CENTRE the pivot. Now you can apply your lattice. Modify your lattice to shape the eye as you please, then take both lattice nodes and parent them to the eye-Locator. Now, wherever the locator goes, the eye lattice goes, likwise, you need to parent the eye geometry Group node to the locator also.
...now, as a result of parenting to the locator and matching all the pivots centrally, you can freely move the locator (whole eye) and the eye and lattice move together and rotate together. Your Aim constraint should be working, if not, you did not apply the correct setting to one axis in the aim constraint options. Heres the fun part....as a result of applying your lattice to the group node, anything within that group now has a local axis assigned to every vertex in theory, within the lattice. In other words, everything is relative. So, you can rotate the eyelid and it will remain consistant with the shape of the eyeball, and you can move your aim constraint to rotate the eyeball itself, again maintaing the correct shape. There you go. Any questions, I suggest you try to work out the answers yourself first....there would be no fun if I told you everything now would there.