Lilly and other traditional Astrologers did attibute physical characteristics to signs. For example he says that the shape and description of Taurus is:
'short but of of a full strong and well set stature, a broad forehead, great eyes, big face, large, strong shoulders, great mouth, and thick lips, gross hands, black rugged hair'
Now reading Lilly's work on Natal Astrology it is clear that he did not just take the basic sign physical descriptions in his nativities, he adjusted for a variety of planetary conditions. He takes (in order):
1. Planets in the Ascendant
2. Ascendant sign, (and intercepted sign if any)
3. Ascendant ruler
4. Planet or planets aspecting the Ascendant ruler (in partile degree)
5. Fixed stars rising with the Ascendant
6. Temperament
On this basis the Sun would have a role in the process, if it were in the Ascendant, otherwise it would not have any role to play except to the extent it contributes to Temperament.
Moreover, he recognised that whilst it might work well for natives from England, it didn't work anywhere near as well if you were dealing with a native of Southern Spain or someone from North Africa. In his day, I guess the number of 'non-standard' types an Astrologer met, was miniscule - these days we live in multi-cultural societies and one cannot be anywhere near as certain as Lilly was - assuming he invariably got it right.
Lilly would only have agreed with the modern interpretation of the Ascendant as how others see us in a literal sense and even then he'd say it was far too simple an approach. Of course psychological Astrologers would argue that it's much more than that.