NPDA transitions to different states by taking same input and popping same top element of a stack
This is very well possible, the automaton nondeterministically chooses which transition is taken. So it may choose between $\lambda$-transitions and transitions reading input, all with the same symbol on top of the stack.

Sometimes this is written as 
$\delta(q_1,a,A)=\{ (q_2,A), (q_3,Z)\}$,
where $\delta$ is considered as a function from $Q\times(\Sigma\cup\{\lambda\})\times\Gamma$ into finite subsets of $Q\times\Gamma^*$.

Alternatively $\delta$ can be seen as a finite relation in $Q\times(\Sigma\cup\{\lambda\})\times\Gamma\times Q\times\Gamma^*$, and we write $(q_1,a,A,q_2,A), (q_1,a,A,q_3,Z)\in\delta$.