Geometric Cryptography and Zero-Knowledge Proofs
Suppose that the second approach is used, this would allow an attacker to impose Alice. The intuition is that, as long as an attacker knows what is Bob going to ask him, he will be able to make things as he wishes in order for verification to pass.

Basically, the attacker wants to give Bob a (chosen) value of $R$ such that when he gives $L'$ to Bob verification holds ($L'$ would be $L = K + X_A$ in the case of Alice). This means that $3\ast L'$ should be equal to $R + Y_A$. This is easy since he can choose at first a random value for $L'$ and then set $R$ to be $3\ast L' - Y_A$ (recall that $Y_A$ is public!), you can check that verification will pass.

Notice that this works since the attacker sends $L'$ and $R$ simultaneously. This fails in the former protocol since Alice is asked to commit to $R$ at the beginning and then compute $L$ from there depending on Bob's choice.