I’m not sure of the dates, but at some point (which must have been before 2013), Chiltern became responsible for providing the service for the stations after Dorridge, so Lapworth to Leamington Spa, with all 3 local services terminating at Dorridge. In order not to slow down London services too much Chiltern decided to provide the local 2 hourly Leamington to Moor Street shuttle, which alternated with the Leamington to Stratford shuttles. (The shuttle introduction may have happened after the transfer from London Midland to Chiltern for Lapworth etc.
The in 2013 with the opening of Stratford Parkway station one of the Dorridge terminators was extended to Stratford, but it omitted Lapworth, maybe because of low forecast traffic or maybe pathing difficulties between Hatton and Bearley junction or maybe just “Not one of our stations”.
With the recast timetable the Lapworth stops have been added, whilst the Chiltern 2 hourly shuttle remains.