In the intended case, the proxy server will forward the attackers flood attack to the target. This means that the proxy experiences as much incoming traffic as the target, plus as much outgoing traffic as the attacker, so the attacker will hit the proxy server twice as hard as the actual target.
However, most proxy servers use caching. This means when the same URL is requested multiple times from the same website (like LOIC does), the proxy will only fetch it once and then serve its local copy without contacting the destination again. In that case the attacker will only consume resources on the proxy, and not on the target site.
In fact, setting up a lean reverse proxy with caching enabled in front of a web application is standard procedure of defending against DDOS attacks. By using a caching proxy server on the client-side, the attacker does that for the target.