Being a good neighbor involves awareness of one's own impact. It seems your neighbor struggles with that. Porcelain berry is an invasive species that is very hard to control once established, so your proactivity is a good idea. Some states even have specific pages dedicated to controlling and removing the vine.
You may want to search your state's Department of Agriculture website for help. Talk to your lawn crew about your specific concerns regarding the tree and see if this is something they can handle.
Per Trees Atlanta, an organization dedicated to planting, conserving and educating the public about trees, one method for removing porcelain berry is to unwind the vine carefully from the branches and trunk, with gloves and clippers.
Once the vine is unwound, they recommend cutting the vine at the base, which will kill the vines that are beyond reach. They recommend not trying to pull down vines that are above the reach of your hands.
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