I forgot to mention that the oval Leman cap box is available from TOTW. Part Number: PB-MA-10-B
I like the second one above but it looks like that may not be correct for a flint lock?
Early students of Leman rifles thought there was a chronological order to the style of patch/cap boxes that Leman used. The four-piece patch box shown above was thought to be the earliest. The oval 4-screw cap box shown immediately above was thought to have come next. Then the 2-screw fleur-de-lis finial was the last one Leman used.
Further study as additional rifles were collected showed that the concept of orderly development of the patch/cap box did not fit actual specimens. Several flintlock rifles came to light with locks dated 1840 that had the 2-screw fleur-de-lis finial cap box. Keep in mind that Leman didn't go into business on his own until 1834, so in only six years he had developed his classic architecture and mountings that he used until his death in 1887.
Jack Brooks, who has his version of the classic Leman Indian rifle and has had many Leman rifles come through his shop for repair and restoration, has said that it almost appears that the Leman workers had buckets or bins of parts near their work bench and they put on the rifle they were working on whatever they happened to grab from the bucket. In other words, he's seen rifles with a diverse mixture of parts.
I don't have a picture at hand of an oval 4-screw cap box on a Leman flintlock rifle, but there is probably one out there. There certainly are flintlocks with the 2-screw fleur-de-lis finial cap box, which used to be thought the latest style. The lock on the rifle pictured below is dated 1840.