No NN2 will not use L1 for its training, it just uses Out1 in its loss L2.
In the given scenario, Out2 and Out1 are inter dependent, Object/obstacle tracking and ego path estimation are correlated tasks, however NN1 (object tracking network) need not have the same loss as NN2, it just uses NN2-Out2 for its own loss (L1) calculation.
Think of it as an unsupervised cross task scenario.