Question
How do the locus trees root underground?  Do they root toward the foundation of the home?

Answer
Tree roots will grow toward a water source. locust roots are in generally small and fibrous. Generally if the foundation does not have cracks in it the foundation will not be bother by locust roots. The area near foundations will be much drier than the soil away from the building so the roots will grow away from the building seeking water. Usually the roots system extents about 1 1/2 times the width of the foliage. You should not have a problem with the root system and the foundation of locust but they will sprout aggressively form the roots and you may have a problem with these sprouts coming up in your lawn.