Solving Euler Equation for standard DSGE Models
It really depends on the problem. As to why it would disappear, sometimes you can express the multiplier in terms of variables at the present or past, as in $\lambda_{t+1}=\lambda_{(c_t,n_t,M_t)}$ , which means it's an expectation over values that are known at that time. Therefore, you have $E_t[\lambda_{t+1}]=E_t[\lambda_{(c_t,n_t,M_t)}]=\lambda_{(c_t,n_t,M_t)}=\lambda_{t+1}$

But, as said above, it depends on the problem.