Why ++variable isn't treated as lvalue in C?

Question

Consider the following C code:

#include <stdio.h>

int main(void) {
    int a = 0;
    printf("%d\n", ++a += 1);
}

++ has precedence over += so it should be evaluated first. So we have a on the left and 1 on the right. Now based on my understanding ++a should result in a (only changes its value) which is lvalue so why this statement gives the following error:

lvalue required as left operand of assignment