Ok. Well, let's start simple. Say that the two beams are focused to a point (don't ever focus a point on your LPM, though) on the same spot. Say both lasers are identical wavelength and identical power, for convenience. Shine 1W from laser 1 and 1W from laser 2. What is the optical power incident on the spot? If the two light beams strike the spot with exactly the same phase angle, the two beams will add up perfectly to 2W. If the two light beams strike the spot with exactly opposite phase angles (180° difference), the two beams will cancel perfectly to yield 0W.
Next, say that the two beams are focused into spots of identical radius and identically centered, and the two sources are exactly the same distance from the spot from exactly the same opposing angle. For the exact center of the spot, the same principle applies, but for everywhere else within the spot, there is a difference in distance from that point with in the spot to the two lasers. If the two lasers are perfectly in phase, the center of the spot will be twice as bright, and a point half a wavelength away from the center will be completely unilluminated by the lasers, because the beam incident at that point will be phase shifted by 180° between the two beams. A point one which is situated with a difference in distance from the point to each of the lasers of exactly one wavelength will again have perfect constructive interference, because the light travelling from the farther laser completes 360° of an extra wave, placing it back at the same point in the waveform. So, ultimately, you would see a bright spot in the center, then dark rings every odd number of half wavelengths in radius, and bright rings every even number of half wavelengths in radius.
If you move one laser slightly, so that it is farther away from the spot, and, say, refocus it such that the spot size remains constant, the only thing that will change about the situation is that there will be an offset in the "home point" of the fringes from the center of the spot to some ring of radius whatever within the spot. The perceived power of the entire spot would be the root mean square of the sum of the lasers power, or the square root of two, 1.414...W.
If, on the other hand, the two lasers are not exactly the same radius or centered exactly the same or perfectly aligned perfect circles, there will be some area around the spot where both lasers are incident where only one laser is incident. Since there is no interference in that area, the perceived power there would be 2W.
Since I can only assume that the two lasers will never be perfectly aligned spots with perfect overlap, the resultant perceived power must be somewhere between the square root of 2 and 2 times the laser's individual powers.