I once lined one of these reasonably successfully as follows:
1) Paint coach crimson.
2) Brush paint the raised panelling gold.
3) Spray the side with matt varnish. This allows a suitable key to....
4) Put in the black centre of the lining with a Rotring pen and black ink.
5) Varnish to taste.
I think the clerestories will be easier than the arc roof ones, as, IIRC, they are Clayton square panel ones, so you don't have to worry about curved corners to the lining.
The lettering will depend on the period you model (I'm talking Midland here - I know nothing about LMS)
Prior to 1906, I think they would have a small san serif 'MIDLAND' in the waist panels, with the class designation spelt out as 'FIRST' and 'Third' in the waist panel of the door.
After 1906 they would have a Serif 'MIDLAND' on a black panel under the eave of the roof, about in the middle, and large numbers 1 and 3 on the doors. Lining would be gold pre WW1 and yellow afterwards for non corridor coaches.
Bill