I live in west Essex, England. Several years ago I planted a group of three Liriope muscari in partial shade in very heavy clay soil. They flowered the first year, but have not done so since and haven't really spread much, though their foliage is reasonably healthy looking. Any ideas why this might be? In the same bed and thriving are Geranium 'Rozanne', Persicaria 'Firetail', Rosa 'Graham Thomas' and Fatsia japonica.
The other plants you've used will be perfectly happy with heavy clay soil in partial shade, but Liriope prefers a well draining soil which is fairly rich - usually achieved by incorporating composted manure prior to planting. It also prefers quite a bit of sun, so although it will grow in shade, it may not flower well. There is one Liriope that flowers happily in total shade, and that's Liriope 'monroe white', but even that does not appreciate really heavy, damp soil, so the soil is likely the main problem.
You could try digging it up and digging in horticultural grit and plenty of good garden compost, soil conditioning compost from the garden centre, or well rotted manure, but its not likely to be that effective unless you do this to the whole area, which would mean removing the other, smaller plants in the area first as well. Otherwise, if you have an area with better soil, move it there, grow it in a pot, or just leave it in situ for its leaves.