This is not going to be easy.
According to the Hawk set up parameters, the horizontal wind average and vertical wind average are both settable by you (under Vario Parameters), and default to 30 seconds horizontal, and 10 seconds vertical. You need to check your specific settings. In addition to that, you have his (Heinrich Meyr) Kalman filter algorithm which takes a noisy signal from the IMU and uses a filter variable (which he calls the "wind variance") and smoothes the values. If you really want to dive into the math, you can get to it here:
https://en.wikipedia.org/wiki/Kalman_filter assuming that Heinrich didn't alter the base algorithm too much. Fair warning, he refers to it as an "advanced Kalman filter"., implying that he took it beyond the basics.
If you have ever worked with IMU x/y/z data, you know how insanely noisy it can be, and is kind of amazing that it cleans up with averaging.
Next up, we have the LX logging algorithm, which might be storing the values at the beginning of each second, somewhere in the middle as they are recalculated, or at the end of each second, and then writing it to the log file. That could account for at least 1 of the 2 second discrepancies you are seeing. I don't think they were intending for the data to be analyzed down to that detail. One of the biggest limitations I found, was the accuracy of the GPS signal vertically, which is much worse than horizontal resolution. Since all of the GPS satellites are in effect on the same side, the vertical resolution just isn't fine enough. Generally +/- 2 to 4 meters. While they do record to a tenth of a meter in the IGC file, that doesn't mean it is accurate to that same degree. For this same reason, the actual lift you are seeing during playback can be significantly different than what really happened. This is why GPS vario's (like in Navigator or Oudies) are notoriously bad, and why any respectable vario has to have a pneumatic source.
If you try to calculate the altitude by accumulating the vario numbers, and compare them with the GPS altitude (or even the pressure altitude), you will find one of two things:
a) either they drift apart significantly over time (hence the nature of the inherent errors)
or
b) they match, which means that LX is back calculating the vario numbers from changes in the pressure altitude
I personally think they are doing a), but I haven't checked.
If you want to see how noisy that data is, try plotting the lift vs. the speed, and comparing that to the polar curve, and you will see it jumping about so wildly, that you couldn't ever hope to derive a polar from the actual data. Or, just plot the VAT and NET values over time (you can even doo this in SeeYou), and look how noisy the vertical data is:
That was from a recent flight, and there was nowhere near +/- 14 knots of lift/sink.
If what you are trying to get is the yellow convergence vector, it is just the difference between the instantaneous wind, and the average wind. But the tails of those two vectors together, and you get the yellow vector. In essence showing a short term gust, which in theory is pointing toward an area of higher lift. I have not found that nearly as effective in tracking convergence, as just paying attention to the crosswind component of the average wind, but it has seemed to help in determining which way to go when approaching a thermal.
All that said, not sure if any of this helps at all, but there you have it. There is way more art than science in the interpretation of the noisy data.