I remember learning that there may be an issue of using two halachos L’Moshe M’Sinai at the same time (Rabbi Akiva Eiger maybe?). Halacha l’maaseh can one make a sukkah employing lavud and gud asik which is very commonly used by many?
R’ Akiva Eiger (Shut) 1-12 says it regarding the opinion of the Ran regarding dofen akuma and gud asik, that if the wall doesn’t reach the sechach, and part of the foor is sechach posul, that it is not kasher because it is two halachos L’Moshe M’Sinai (see MG”A 632-1 and M:B 632- 4). However see R’ A. Eiger on the Shulchan Aruch 632-1, that he asks on the Ran because sometimes we do say use two halachos L’Moshe M’Sinai, such as in 630-9, that it is permitted to put a piece of wall a little more than 7 tefachim a little less than 3 tefachim above the ground, which will make a wall of 10, even though the top of the wall doesn’t reach the sechach. This would be using gus asik and lavud in order to make the wall useable, so we see not like the Ran? The Achronim answer that there is a difference between the two cases. When the roof that we want to use the rule of dofen akuma has an air space, then we are saying both halachos for the same exact place. However, in 630-9, the bottom of the wall is using lavud, and the part of the wall above 10 is using gus asik, since each place is only using one halacha L’Moshe M’Sinai, then everyone agrees that it is permitted. Getting to your picture, it would be the same thing there, the part below ten needs lavud and above ten needs gud asik, therefore the issue of 2 halachos will not be a problem. (As a side point, if we are going to use gud asik for the wall, it will have to not be removed from the edge of the schach, because otherwise we would need lavud and gud asik in the same place, the upper corner, and it would be a problem. See 630-9 and M:B 44).
There may however be another issue with such a Succah. That if the walls are made only of horizontal or only vertical poles with air between the poles, according to some poskim it is problematic. (See Bikurei Yackov 630-4, Bais Meir beginning of siman 630, Chazon Ish O:CH 75-12, Kovetz Halachos (Succah) 3-17). However others (MG:A beginning of siman 630, M:B 630-7, Aruch Hashulchan 630-18) say that it is permitted if the succah has four walls, however if the succah only has three walls then even according to them it is problematic. Therefore, if someone has such a succah, and it has four walls, it is controversial, but one can rely on the opinions that it is permitted. However, if the succah is only of three such walls, it shouldn’t be used without the canvas that it comes with, and one should make sure that the bottom ten tefachim (until after the poles on the bottom) are tied well so that the tarp doesn’t flap around in the wind. Then it would be considered a full wall. (Alternatively, one can put vertical pieces of wood, spaced less than 3 tefachim apart, and then the wall is not only vertical or horizontal poles, but both, and then this wouldn’t be an issue.)
Have a kasiva v’chasima tova.
Bikurai Yackov 632-2, Chazon Ish, O:CH 77-7, Emek Bracha pg. 84. See Kovetz Halachos (Sukkah) 3 ftnt. 33, that discusses R’ Akiva Eiger.