Hi. Based on its smooth, light grey bark and its large, oblong leaves that have entire margins, I suspect it is a type of magnolia. The species Magnolia liliiflora have a variety of common names, one of which is Japanese magnolia. Its flowers are large and purple, so that’s probably what you have. (Note also that you described its flowers as lily-like, which is what its specific epithet means.) Your shrub could also be a hybrid between M. liliiflora and another species. Here is an example of a hybrid from the Missouri Botanical Garden. It has a good photo of a typical flower. This page from Washington State U. provides some more information about the species.