If Lilly was conversant with "Sidereal" to any extent (in terms of written material from the past) then this might have been one of his choices. I don't see how (in my limited knowledge of the subject) he could have used any of the Indian base systems for fixing the Sidereal Zodiac.
He didn't use an Indian system, I did
(as I noted in my post) - to get an Ascendant that fitted his description (though he did not give a degree of Gemini for the 'Ascendant'. In the body of his work he only assigns degrees to Signs - i.e the tropical zodiac. At the end of his book he gives the longitudes of the constellations and he quotes Gemini as being:
The first part of Gemini is from the 26th og Gemini to the sixth of Cancer The stars in this part are mostly harmful, yea even in our days
The middle part is from the sixth of Cancer to the fourteenth of Cancer, containing Saturnine stars in the arms and knees of the Twins, These are temperate inclining to dryness.
The latter are from the fourtheenth to the twenty fourth of Cancer, these are mixed and uncertain stars declining to dryness because of some Saturnine, some Martial and some Mercurian stars.
It is this latter part that he attributes to the Cancer Ascendant at 16 degrees 50 of Cancer
It's also clear from this whole list that he has no common factor for precession of the 'asterisms' as one would have for sidereal signs - for example he starts the 'asterism' of Aries at 28 degrees Aries as against the 26 degrees of Gemini where the 'asterism' of Gemini begins. The 'asterism' of Taurus on the other hand begins at 17degrees Taurus and continues to 25 Gemini, some 38 degrees. He's dealing with constellations on the ecloptic, not signs (either tropical of sidereal) here. And as I said in my last post I was wrong to say that he he seemed to use a sidereal zodiac as an alternative
Now all definitions of constellations are arbitrary in terms of longitude and latitude and indeed the Astronomical community have revised these several times since Lilly's day. So there are issues both in terms of his definition of the beginning and end points in themselves and the accuracy of scientific instruments of his day to measure these distances accurately (as you said) and indeed to measure time accurately - you will note that Lilly gives his chart a 16 degrees 50 Ascendant in Cancer and an MC of 15 degrees 46 Pisces. Solar Fire gives the Ascendant of 21 degrees 13 Cancer, and MC of 19 degrees 12 Pisces. or a little later than Lilly thought (assuming that modern computer algorithms accurately project backwards 360 years), or more likely there are small errors in his tables.
On the issue of the accuracy of measurement, the problem is compounded by how we define the beginning and end of these constellations. Lilly does advance a definition but he can't be blamed if Astronomers a couple of hundred years later chose to redefine those constellations. Where there are errors in measurement in the seventeenth century he's a victim of his time.
Should we use these definitions now? Only if we wish to check what a Lilly method prediction would look like compared to a modern prediction (though as there are a whole host of other differences between Lilly and a modern Astrologer, it's difficult to say that this will yield a major difference).
It's of course easier where Lilly mentions a particular star, because that stars modern placement can be identified and adjustments made for it's movement since Lilly's time.
My view is that he implicitly recognises precession but does not advance any reason for the discrepancies in the longitude of the constellations compared to the signs that he notes. Whether he does it in other works I don't know, it certainly does not occur in Christian Astrology but there is a third great work the 'Prophetical Merlin' which deals with Mundane Astrology and he might touch on it there. I've not seen that work in print but I'm hoping to get it at some point.