Lapping with paper is not effective except for finishing. Once the surface is flat then paper can finish a stone face.

For lapping you need loose grit, either Silicone Carbide, inexpensive from Got Grit.com, ($15 for a progression) on a steel cookie sheet. Get flat with 60 grit, or loose Diamond on MDF, imbedding the grit in the flat, softer MDF.
Once flat a progression of Diamond or Silicone Carbide grit will go quickly. Finish on Wet & Dry to the highest grit for the finish you are after.

60 grit loose Silicone Carbide will get most Ark stones flat in 20 minutes or so. There are many threads on lapping Arks.