For $L_1$ we count $xy$ using stack and if after $y$ another $y$ comes, it marks the start of $yz$ and then we start popping the count from stack. So, this is DCFL. (changing $xy$ to $yx$ would make it non-DCFL).
For $l_2$ we need to see if $\#a \neq \#b$, so we push $a$ on stack and pop $b$. So, DCFL.
D choice. (All other choices are also correct).