An irrigation company, in order to get to a sprinkler head and pipe, grinded several roots from my neighbors oak tree. The tree is at least 6' around at the base and the trunk divides into three trunks and one of those again into another. It is on a hill and leans slightly towards my home. The repair was done two feet away from the trunk. All roots were removed 12" to 15"s down and approximately 40"s wide. I am worried that this tree has been damaged as well as compromised and might fall on my home in a storm.
You don't say what part of the world you're in, and that makes a difference to legal procedures, but if the tree is close enough to damage your house should it fall, here in the UK, I'd advise my buildings insurance company of what's happened, and hopefully, they'd either arrange for a Tree surgeon to attend and assess the situation, or pay for a tree surgeon to come out and assess. If it is considered a danger, the insurance company will then take steps by approaching the neighbour and have the tree removed or whatever is the right thing to do depending on the Tree Surgeon's advice.
It sounds as if they removed a significant amount of root material, including some large roots, and that is, as you fear, very likely to compromise the tree.