Given that Grandad has not been able to care for the trees for 3 years I would be planning to repot in Spring. The soil will be old. Likely the roots have filled the pot, leaving little space for new roots , water and air to penetrate into the soil. Even if it does not need repotting it will give you a chance to assess the soil and roots, and, in my experience trees almost always grow better after repotting anyway. Precautionary repot is likely to head of any possible problems next summer, before they occur.
Chinese elms sometimes lose branches for no reason but given that this tree has not had much attention it is likely the branch died from - Lack of light, Lack of water, Too much water or a combination of these. As mentioned, the top of the tree looks healthy so we just cut off the dead branch and move forward with a new shape for the tree.
