As additional evidence that the Doctor in Companion Chronicles is not played by anyone, the Doctor's role is mentioned in the cast for the Early Adventures but not for Companion Chronicles (There were a couple of exceptions when Colin Baker actually voiced the Sixth Doctor, e.g., in Peri and the Piscon Paradox). On the Big Finish website, the same distinction is made but not uniformly: Domain of the Voord and The Bounty of Ceres for some reason do not list the Doctor in the cast.
In addition, the framing device in the Companion Chronicles mentioned by OttselSpy25 above actually has the companion doing almost all of the voices, not only the Doctor's. Typically, there is just one other cast member voicing the main guest protagonist/enemy. This is often described as an enhanced audiobook, which is narrated by the companion who is imitating all voices but one. (There are some exceptions, e.g., Solitaire, that are essentially full-cast dramas for two actors and do not include any narration.)
In the Early Adventures, on the other hand, each role has its own voice actor, but the Doctor is played by the same actor as one of the companions. As for the Lost Stories, I cannot say as I haven't listened to them yet. What I've noticed, however, is that the size of the cast there differs significantly from story to story. I wouldn't be at all surprised if this question in the Lost Stories should be decided on a case-by-case basis.