I could be wrong, but I think there is a very good chance that it would kill the entire pear tree. Not a good idea.

Sheet multch:

http://www.agroforestry.net/pubs/Sheet_Mulching.html

THose "weeds" are bulding soil. IF you smother the weeds with news paper and sheet mulch, youll make some wicked soil for the lawn, and the pear. Maybe a good time to throw in a few new planting beds?

I avoid round up. Most herbicides end up in the ground water, and kill good insects and soil bacteria.

No, it won't be taken up into the pears and poison them. Roundup binds very tightly to soil particles and isn't taken up by roots. Any contact with "green" aka young bark or foliage will damage or kill the tree.

Honestly, though, is his existing lawn so far gone that it couldn't be rehabilitated by use of a broadleaved herbicide (once again avoiding the pear tree) and proper turfgrass management techniques?

Ray:

I spray roundup underneath my 18 fruit trees and they grow just fine. I use it to kill off all weeds growing under the trees. Many orchards commonly spray an herbicide under their orchard rows where I live.

The roundup should not kill the pear unless you have any
root suckers growing up at the base of the pear. You want to avoid spraying any roundup on the pear leaves. When I spray, I use a cardboard shield close to the truck to avoid
any spray on the trunk as well. Old trees with thick bark are less prone to injury but using Roundup around young apples can be an issue. I learned this the hard way years ago spraying roundup around young Golden Delicious apples.

The spray went thru the bark as the the trees showed stress
symptoms and dropped leaves in September for two years after that. The University Fruit Exension agent visited and said it was from the Roundup. After that I always
use a piece of cardboard as a shield when spraying Roundup
around the trunk of young trees.

Denninmi is right in that Roundup is supposed to readily break down with soil contact.

I appreciate everybody's input here. Thanks so much!