You can just do some sorting and grouping with vertex coordinates.

g = TreeGraph[
  RandomInteger[#] \[UndirectedEdge] # + 1 & /@ Range[0, 30], 
  VertexLabels -> Automatic]

coord = Thread[VertexList[g] -> GraphEmbedding[g]];

layers = (SortBy[#, #[[2, 1]] &] & /@ 
     GatherBy[Reverse[SortBy[coord, #[[2, 2]] &]], #[[2, 2]] &])[[All,
     All, 1]];

Column[layers]

Hi Richard, I don't know (I'm not an expert alas). There should be :)

Anyway I always thought that for the LayeredEmbedding the RootVertex chosen was one of the Vertexes with the lowest VertexEccentricity.

Playing with the random graph written by @Jaebum Jung this might be right.

{VertexEccentricity[LEgPP, #], #} & /@ VertexList[LEgPP] //Sort // First // Last

seems to do the trick for your graph and a couple of the randomgraphs I tried. Using on Graphs with some disconnected Vertex will not work (unless you cast out the ones with 0 Eccentricity first). I think that Jaebum's way will be the fastest way of sorting it out anyway. But if you Use the option GraphLayout -> {"LayeredEmbedding", "Orientation" -> Left} it will fail and mine will still work. Obviously Jaebum's way will work with changing the sorting order.