1) There is a limit to how much you can remove before most people will think the tree looks unnatural/weird. Different people may have different ideas about the "ideal" look. Don't prune higher than you think it should be. Based on your description and without a picture, I would tend to agree with you that the tree is already pruned up about as much as I would want to prune it up.

2) YES!!! Always completely remove limbs or at least cut them back to a crotch with a branch of at least 1/3 the diameter of the main limb. Stub/heading cuts result in an inability for the tree to cover over the wound before rot sets in.

3) Pretty much.

4) NO!!! Thinning and pruning up will result in more top growth and increase the the likelihood of wind damage. Your neighbors are just trying to get their way by saying anything they can think of. Based on your description, they seem misguided.

5) Some types of grass do much better in shade than others, if you neighbors insist on grass and you decide to let them have their way. It does seem a shame that they can't work with you to optimize the landscape there.

Thanks for the reply brandon.

Unfortunately, a good number of branches (30% of the tree) hang over the neighbors property line and by law, they have a right to trim them. I tried talking them out of this to no avail, so I agreed to cut the branches short where they requested it. (They may have pruned more branches than I cut that day for all I know.) These were mid branch cuts, which I knew was bad, but I don't remember seeing any obvious crotches like the ones you described at the time. I'll have to inspect them again.

So let me ask you this, if I can find no crotches where there is a an offshoot which is at least 1/3 the diameter of the branch I am cutting, would it be better to leave the stubs, or just prune the branches back to the trunk. The cutting that I did has already made the shape of the tree somewhat unbalanced. If I were to cut those branches back all the way to the trunk, I'd wind up with a tree that has a very lopsided bottom half. These stubbed branches are probably up to 15 feet off the ground. Not sure what to do now.

Tree health wise, you'd be better off pruning the limbs back to the trunk.

One would think that the nutty neighbors would not like looking at such a mess. I guess this is just another example to show that, when we plant trees, it's probably best to plant them so that their canopy does not extend into the neighbor's yard (when possible).

True. Too bad I didn't plant it though :(

One other question. I may start a new thread for this if I don't get an answer here. Over the past few years the neighbors have cut down 2 large sycamores which shaded my LLL for half the day. Last summer, the tree finally had sun from around 10:30 am (when the sun makes its way over my house) until 7:30 pm. That summer, for the first time, the tree had the most glorious smell and attracted literally thousands of bees. We loved it. Last summer the neighbors also added a few inches of top soil and grass within a few feet of the trunk. This only covers maybe 35% of the root zone.

1) should 't mature LLL bloom/smell like every year? This year we got the light green pedals and little yellow balls but no smell or bees.
2) was it the extra sunlight that pushed it over the edge last summer
3) was it the extra soil that is preventing it from doing it this year?

Thanks again

Edit to above post.

Most of the light green pedals attached to the little yellow balls, which I assume are flower buds, have already fallen off the tree. It looked like only some of the balls had bloomed. So what made them bloom, stay on, and smell so well last year, and why hasn't it happened before or since? We did have that incredibly long and cold winter this year.

Hmm.

Well, adding soil over top of the root zone is bad. It may or may not hurt the tree, depending how deep and how much, but it's not a good thing to do - the tree grew its roots at the depth it wanted to. Too much soil piled on can reduce air flow and smother them.

As far as grass underneath, Lindens IME are as dense as maples when it comes to shade - neither is a good tree to grow grass under.

Remember this tree is on a slope where there is a lot of rain runoff. The soil had eroded and roots had been uncovered unaturally quickly. Some of the soil was just to level the yard again and cover the roots.

Speaking of trees that aren't good for grass, what are examples of ones that are good? I have a thornless honey locust that is struggling at the end of my deck. It loses all of it's leaves by september, and sheds stuff pretty much for the entire green season. It's a mess. I'm thinking of cutting it down and planting something a little further away from the deck. It would be on the east side of my house, at the bottom of a slope, getting sun from 10:00 til 2:00 until it's taller, in acidic clay soil. The deck is a 5 feet higher, so I'd like something that grows up and out, and provides medium shade. Something that isn't super messy or prone to issues would be great too. Any suggestions?