$C_j = 1/s_j \sum_{i=1}^n w_iJ_i^j$.
$w_i$ is some (real) number. $J_i^j$ is a 0-1 random variable and the P($J_i^j = 1)= p_i^j$.
$l_j = 1/s_j \sum_{i:[n]} w_i p_i^j$. This is a sum over all $i$. (Both summations are over all $i$. So there are $n$ $i$'s). Intuitively, $i$ are the number of tasks to be completed.
What is the difference between $l_j$ and $C_j$? If so, what is it?
Looking solely at your formulation and taking $s_j$ to be a fixed, real number >0:
The main difference between $C_j$ and $l_j$ is that the former is a random variable while the latter is the expected value of $C_j$. By linearity of expectation:
$E[C_j]=E[1/s_j \sum_{i=1}^n w_iJ_i^j]=\frac{1}{s_j}E[\sum_{i=1}^n w_iJ_i^j]=\frac{1}{s_j}\sum_{i=1}^n w_iE[J_i^j]$
Since $J_i^j$ is an indicator variable with $P(J_i^j = 1)= p_i^j, P(J_i^j = 0)= 1-p_i^j$, we get: $E[J_i^j]=p_i^j\rightarrow E[C_j]=\frac{1}{s_j}\sum_{i=1}^n w_iE[J_i^j]=1/s_j \sum_{i:[n]} w_i p_i^j =l_j$