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It seems to me that there are 3 ways to to lunars:

The traditional method, 

Chichester's method,

Letcher's method.

I don't know how accurate the traditional method is generally.

My recollection of  Chichester's is that the lines of position cross at a relatively small angle (20° or less)  and resolution of longitude is on the order of 20-40nm.  I forget the exact method.

Letcher's method has you calculating a round of stars and the moon adjusting time forwards or backward for all of them until the moon line runs thru the center of the round of stars.  Since you are dealing with inaccuracy in the moon line of several nautical miles, the moon line is moving relative to the star lines on the order of 1.9nm/min then the best reasonable resolution of longitude is 15' and probably a lot more.  As a means of re-establishing time while at sea, it will get you within a couple minutes. 

If you can use one of the methods to reach a known fixed position, then you can reestablish better time by shooting the sun or other bodies from the known position and working backward you can probably get time back to within 5-10Sec.