Is it reasonable to consider adding a foundation walls to an existing home to replace the existing aluminim siding with 3.5 to 4 inch stone siding? The existing home is approximately 1350 sq. ft. on the first floor.
I believe you usually add a lentil or a ledge to the existing structure for the new brick to rest on. I don't think a new foundation wall is usually necessary, but you'll need to check with an engineer.
A LINTEL is a beam intended to span an opening in a masonry wall, so would not be used in this situation. Similarly, you can't just build 'a ledge' to sit the masonry on without being specific as to how you fix this 'ledge' to the existing structure.
We do not know the height the cladding will need to be (eg does the OP's house have tall gable walls?)
The cladding will represent a considerable extra load and will need to be properly supported. The only effective way is to extend laterally the existing footing by fixing rebar into it and casting concrete around the projecting bars. The design/specification of this is an engineer's job.