According to the Rob't Elliot Lefever books, the H grade, DS grade, and I grade guns were all probably introduced in 1900 at around serial number 31632. This makes sense because the large cocking hook was introduced in 1899. We also know the I and DS were introduced shortly before Dan Lefever's departure from Lefever Arms Co. in 1901.
I've bought a few of these unusual DS grade guns that have characteristics typically found on the H grade, including Twist barrels with an H stamp, cocking indicators, and Dolls Head barrels and frame. The examples I own have the LAC monogram buttplate found on the H grade, and one has a capped pistol grip stock. This one has the ring groove buttplate seen more often on the I grade and some DS grades.
There are several theories about DS grade guns that have H grade features, including that they were all assembled out of sequence by Ithaca Gun Co. after the sale of Lefever to Ithaca in 1916.
I don't believe the theories that claim every unusual Lefever must have been assembled out of sequence or assembled by Ithaca. I think it is absurd to think that Lefever Arms Co. had thousands of mixed and out of sequence serial number frames and parts on hand at the time of the sale. I believe that Dan Lefever and his business partners fully understood the concept of serialization... and that doesn't involve randomly stamping frames with numbers that would place them many years apart in the production sequence. It means numbering frames in a logical numerical progression.
I do believe it is entirely possible that a small number of guns were finished and sold out of sequence due to things like using frames as prototypes to try new features. I suppose a small number of frames could get misplaced during the assembly process too. Mistakes were also made. Around 2010, two Lefever guns appeared on Gunbroker at the same time with the same serial number. One was in Pennsylvania, and the other was in California. One was an Optimus Grade, and one was a G Grade. The Optimus sold rather cheap at around $17,000 because of the fear that it was an illegitimate upgrade, but after the sale, it was judged by knowledgeable collectors to be legit. The same Lefever collector bought both guns.
That said, I tend to believe this particular DS probably was assembled out of sequence, and also was assembled by Ithaca... for two reasons:
1) I think it is possible that this particular frame with the 50,000 serial number may have been set aside to build a high grade, special order, or presentation gun, since 50,000 would be a milestone of sorts. But that didn't happen for some reason, and it remained in the factory until the sale and transfer of parts inventory and equipment to Ithaca.
2) This gun also has the letter "T" stamped on the forend hanger, which is one common indicator of Ithaca assembly.
This is my THEORY, and an educated guess about this gun. After years of collecting and studying Lefevers, I have learned that nobody knows the full story, and many things are stated as fact without a shred of evidence.