In ASP.NET 4 this was as easy as routes.LowercaseUrls = true; in the RegisterRoutes handler for the app.
routes.LowercaseUrls = true;
RegisterRoutes
I cannot find an equivalent in ASP
For ASP.NET Core:
Add the following line to the ConfigureServices method of the Startup class.
ConfigureServices
Startup
services.AddRouting(options => options.LowercaseUrls = true);
Thanks to Skorunka for the answer as a comment. I thought it was worth promoting to an actual answer.