I have some old Lily of the Valley plants around the northeast corner of my house, and they grow nice and thick around the foundation, but failed to spread into the four-five foot wide strip along the house which I intended them to. The soil is a damp, heavy clay-based soil with little organic matter. It has been three years now, and sometimes a new shoot comes up in the strip, but they do not last long. The strip is an area mulched with premium bark that goes between four and five feet wide, and over 20' long, between the house and a walkway. Is there a way to to make them spread, or will I have to plant more in the area? It spreads quite well for me in nursery beds and under trees.
You may not be able to make it do what you want - plants grow where they like the conditions, but there is something you can try. Remove the mulch and enrich the soil by digging over and adding humus rich material - leaf mould if possible, but any humus rich stuff will do. This, hopefully, will mean the soil holds onto moisture a lot longer, which will make it more likely that the Convallaria will want to grow there, because it likes deep, fairly rich soil and moist conditions. Deliberately plant some Convallaria in the area - it's usual to dig up and split existing plants anyway, so either do that or buy in some more. You haven't said what type of mulch you're using, but an organic one would be the most useful, so replace the mulch when you're done.
This still may not work - Convallaria seems to like to grow 'under shelter' so to speak, so against shady walls, under other plants, and your strip may simply be too exposed for it.
I had the exact same problem and I planted wild geraniums in the front. My guess was that the lilies grew towards the foundation because the stone of the foundation keeps the dirt moist and a little cooler. I noticed the lilies love to spread their roots/shoots under the pavers of a stone path as well.