First, turn out all of your cooled cake layers, and carefully slice off the bump on the top of each cake so that each layer is flat (you can eat the extra bits). Slice one of the white cake layers in half to make two thinner cake layers, and place one on a cake board or plate. Pipe a ring of the white buttercream around the edge of the top of the cake layer, and fill in with a thin layer of more buttercream. Then pipe a 1/4 inch layer of the lavender mascarpone filling within the buttercream ring, and spread. Place one of the blue cake layers on top, and repeat the buttercream + filling process, this time with the blue buttercream. Continue with cake layers + buttercream + filling (for the Trans Pride flag remember it's blue, pink, white, pink, blue) until you get to the top, extra white thin cake layer.
To crumb coat the cake, pipe the buttercream in rows around the outside of the cake, corresponding to the colors of the cake layers, and then use a long knife or cake scraper to smooth/coat the cake. Freeze entire cake for at least an hour to set the layers/frosting.
Once frozen, pipe buttercream in corresponding color rings around the cake again, and carefully smooth frosting on top and sides per photo above. If you want to press sprinkles onto each color ring, do it now before freezing it. Freeze entire cake again for at least 30 minutes to set this final frosting layer.
Then decorate! You can add both the blue and pink buttercream piping bags to one large piping bag to pipe dual-colored florets around the base and top, adorn with flowers, etc.
Freeze entire cake one last time, for at least an hour, before serving. Let cake sit at room temp for about an hour to defrost before slicing. You can leave the cake in the freezer or fridge overnight if needed.