Adder in LPM seems to be weird

I'm not sure on this (you can check the documentation), but i think the LPM's do unsigned arithmetic. With 2's complement, the output is the same (signed or unsigned) but the carry out is different. Carry out can be thought of as overflow which happens at the 0xffff<->0x0000 boundary for unsigned, but at the 0x8000<->0x7fff boundary for signed. So you can't use an unsigned carry out as the extra bit for a signed add or subtract.

Edit for correction:

Neither carry out nor overflow are equivalent to an extra high order bit for signed arithmetic. Carry out is the same for signed or unsigned, it does not matter which the LPM is using except for the overflow output.