This would probably be a good place to differ with Lilly for a few reasons. I would really like to know his source for this table (and his table for scoring the dignities of the planets for a few reasons), but it isn't given anywhere.
I haven't followed the Lots very much, and
Bonatti's text on it may be more helpful to you than anything in Lilly.
I agree with you on this completely. On the other hand, Lilly was, above all, practical with "correct prediction justifies the technique" approach. In fact, he was ultra modern for his time, I imagine him as a kind of guy who would definitely use modern planets if they had been discovered in his time and he found them to be useful. Many of his conclusions came from his huge practical experience - 2000 charts per year.
Anyway, I have a couple of concerns. Firstly, I wouldn't think the Lots could be Combust for the simple reason that they are not planets and do not have light. It sort of clashes with the philosophy behind Combustion in general. However, I am open to being wrong on this as I am aware the Lots can receive aspects.
Almost all traditional authors unanimously agree that:
1. Lots are accidental dignity/debility sensitive (mostly by house placement)
2. Sign position of the lot matters (in respect to sign qualities: fertile/barren, voiced/mute, male/female etc.)
3. Lots receive aspects but don't cast them
4. Lots can be influenced by fixed stars
The only (remote) reference concerning lot combustion/under the Sun beams I was able to find is in Valens Anthologies, page 28, where he speaks about POF in the 8th house:
"...If Fortune <is there>, the native, besides being dull, will also be stupid and poor,
especially if <the Lot> is under the sun's rays. If under these circumstances malefics are also in conjunction, the native will be deaf and dumb..."
Problem is, the term "rays" was often used to describe an aspect, so this is not entirely clear.
It seems to me that there is no enough evidence to just dismiss Lilly on this, even though he might be completely wrong.
My second concern is much more Lilly-centric in that, you will also see where he has taken the liberty of assigning Signs where the LoF gains dignity, as if it were a planet. Grain of salt there.
Yes, this doesn't make sense at all.
To make matters worse, Lilly does not use the proper calculation for this Lot and the paragraph at the bottom of 145 spells out his feelings towards this Lot's general usefulness. All in all, I'm not sure Lilly really "got" the Lots, and who can blame him when he isn't calculating it correctly?
This mistake goes all the way back to Ptolemy who was the first to introduce this method of POF calculation, so Lilly was probably just following this.