Is there a comprehensive list about which phonemes in the English language can be distinguished via lip-reading and which can't?
Have a look into visemes. These are like phonemes, but relate to what the face is doing (esp. the mouth) for each phoneme. More than one phoneme can map to a viseme (e.g. voiced and voiceless consonants have the same viseme as the distinction is due to the vibration of the vocal chords, not the shape of the mouth).
As far as I can tell, although there was earlier research into confusion of similar phonemes, the visemes were first created by early Disney animators. They defined 12/13 facial shapes for the 45 or so English phonemes. They are also used in text-to-speech applications.
Other classifications can have a different number of visemes,, for example the Microsoft Speech Application Programming Interface (SAPI) defines 21 visemes.
There does not appear to be any clear consensus on the phoneme to viseme classification. I'm not sure what it is like in the lip reading field (a Gamasutra article mentioned there were 18 lip reading visemes, but I was not able to find a reference to this in my brief search, although visemes were mentioned in connection to lip reading in other results).
There is the problem of context, where the shape of the mouth is influenced by the previous and next phoneme.
In addition to this, the simplified viseme model does not account for the shape of the cheeks and jaws, nor the position of the tongue, which can all be visual clues.
The ability to lip read will take the movement of the facial features into account and make inferences based on context (e.g. a t/d shape after
[shi:] could be
she'd). This is similar to how speech recognition software works, but that operates on the acoustic (audio) signal.