S. R. Faruqi:

dil-ḳhvāh = to the heart's content

In this verse is a strange kind of qalandar-like dignity. And there are aspects to the meaning as well. First of all, consider the address to the 'night of separation'. He's spoken as if the night of separation is some intelligent, aware being, and as if it's deliberately burning the speaker.

Then, in the second line, the soḳhtah has both a verbal and a meaningful attraction. With regard to the 'burning' in the first line, it has a verbal affinity. But it can also mean 'cold, grieved', 'extinguished', 'withered', as in Dard's peerless verse:

jald mujh soḳhtah ke pās se jānā kyā thā
āg lene magar āʾe the yih ānā kyā thā

[why did you go away quickly from me, the burnt-out one?
perhaps you had come to take fire-- why did you come?]

Then, soḳhtah can also mean 'kindling wood' (see 'Tilism-e hoshruba' vol. 6, p. 878, and 'Baqiyah-e tilism-e hoshrub'a vol. 1, p. 190; both are by Ahmad Husain Qamar). It's clear that this meaning too is appropriate: that the speaker is burning in such a way, or is being burnt in such a way, as if he would be firewood; or again that the speaker is a log of wood which the fire of separation would blow into flame. (For firewood [īñdhan], see {15,9}.) And soḳhtah can mean a coal, or some kind of thing that quickly catches fire and that is used to light a cooking-grill; this meaning too is suitable.

Now please consider the second line with regard to the roz-e jazā . Here too there are two meanings. The speaker is waiting for the 'Day of Recompense' because on that day there will be compensation for the cruelties he has endured at the hands of the night of separation. But the 'Day of Recompense' can also be awaited because then the 'night of separation' would be punished for them: 'today let it burn me to its heart's content, but tomorrow it will get due punishment.'

The affinity between 'night' and 'day' is also fine. Between dil and soḳhtah is the pleasure of a zila ( dil-soḳhtah , soḳhtah-dil , etc.). The power of the word bhī is worth noticing.

FWP:

SETS == BHI
MOTIFS == DOOMSDAY; NIGHT/DAY; PERSONIFICATIONS
NAMES
TERMS

SRF has pointed out the small elegant touches: the two possibilities of requital ('vengeance' on the aggressor vs. 'compensation' to the victim), the opposition of 'night' and 'day', the multivalence of soḳhtah ('burnt', 'burnt-out', 'kindling', 'firewood'), the possibilities of bhī .

What leaps out is that 'now'. Why 'now'? Now that the lover is so doomed and wretched already that he won't last long? Now that the beloved is irrevocably gone? Now that the lover has nothing left to lose?