Why can't I assign lambda to the variable using ternary operator

Question

When I assign anonymous function to the variable using ternary operator with the true condition, I can call the variable as a normal function.

>>> a = lambda x, y: x + y if True else lambda x, y: x * y
>>> a(1, 2)
3

But when the condition is false and the function to be assigned is after the word else, I get something like this. I have no idea what mechanisms stand behind such a weird behaviour. Is there any syntax nuances? Or any possibility to use ternary operator in cases like this one?

>>> a = lambda x, y: x + y if False else lambda x, y: x * y
>>> a(1, 2)
<function <lambda>.<locals>.<lambda> at 0x10916aee0>