How are you my dear friends.
The following text is taken from the book Christian Astrology by William Lilly.
I understood it almost completely except for this sentence:
[or with that Planet who afflicts any of those]

What did William Lilly mean by it?

[SIGNES CONTRARY, VIZ. OF SICKNESSE, DEATH, &C. MISFORTUNE.]
It’s generally received, that if the Lord of the Ascendant be under the Sunbeams, or going to Combustion, which is worse then when he is departing, or the Moon cadent and unfortunated by any of those Planets who have dominion in the 8th or 6th, and either the South Node, Saturn or Mars in the Ascendant or 7th House, peregrine or in detriments, or retrograde, or if there be in the degree ascending, or in that degree of the Signe wherein the Lord of the Ascendant is, or with the Moon, or with that Planet who afflicts any of those; I say, any Fixed Starre of violent influence or nature of the Planet afflicting, or nature of the Lord of the 8th or 6th House, then you may judge the Querent is not long lived, but neer some danger, or shall undergoe some misfortune in one kind or other, according to the quality of the Significator and Signification of that or those houses they are Lords of. “

Hi there - my sense of this rather complex sentence is this:

If the Lord of the ascendant (ruler of the ascendant) is with a planet that afflicts any of those other significators (those that he lists prior to this phrase) then that's bad news.

So say the Lord of the ascendant is conjunct Saturn, the greater malefic, and Saturn afflicts the Moon by square, then this would indicate a very serious situation for the individual.

It might be helpful to break down the sentence into its components and work methodically through each one:

If the Lord of the Ascendant:

1. be under the Sunbeams, or
2. going to Combustion, which is worse then when he is departing -(that is, the Moon's application to the Sun is more dangerous than its separation from the Sun), or
3. the Moon cadent and unfortunated by any of those Planets who have dominion in the 8th or 6th, and either the South Node, Saturn or Mars in the Ascendant or 7th House, peregrine or in detriments, or retrograde, or
4. if there be in the degree ascending, or in that degree of the Signe wherein the Lord of the Ascendant is, or with the Moon, or with that Planet who afflicts any of those;
5. I say, any Fixed Starre of violent influence or nature of the Planet afflicting, or nature of the Lord of the 8th or 6th House,
6. then you may judge the Querent is not long lived, but neer some danger, or shall undergoe some misfortune in one kind or other, according to the quality of the Significator and Signification of that or those houses they are Lords of.

1 and 2 seem straightforward enough.
3 seems much more complex and seems to combine two conditions - a cadent moon afflicted by the lords of 6th or 8th house AND the malefics (debilitated) in the first or seventh house or the South Node in the 1st or 7th.
4 again is difficult to decipher as you have noted. Hopefully others will come in with their views.
5 - I'm not sure whether this stands alone or refers to point 4.

For reference this comes from Christian Astrology, Chapter 12, p. 130 in the original text.