The OP is proposing to cut out an LGA connection and without even looking I'd bet that it's OK under their fare rules.
Generally, you can standby for a different routing only if the new routing is one that is a legal routing for your fare, like LAX-DFW-MIA in place of LAX-ORD-MIA. LAX-BOS-MIA is not a permitted routing for LAX-MIA, and thus you would not be permitted to standby for it in place of a connection at DFW or ORD.