There are no other airlines which service Los Angeles to Dublin direct. Aer Lingus recently launched the San Francisco (SFO) service. SFO is a hub for United Airlines (though they do have a hub at LA?) with whom Aer Lingus have recently launched a partnership for code-sharing etc. The suspension of the LA service is about forcing as much west coast US traffic into United's hub at SFO.
Unfortunately Aer Lingus will lose money on this because most of the traffic going to LA is origin and destination traffic i.e. most if not all passengers on a regular Dublin to LA flight will have LA as their final destination. Forcing them to now connect at SFO will mean people will be inconvenienced, people will look for quicker alternatives to flying to LA from Dublin.
I'm sure in the near future you'll be able to buy a through-ticket from Dublin to LA via San Francisco on Aer Lingus. However once we get over this economic hump I'd expect some other airline to take up some of the demand for an LA service. Remember there are is a lot of bug business demand in the south west US, airlines make all of their profits from business travellers not cattle down the back.
Your best bets for LA would be to avoid Heathrow and fly either with Air France via Paris or KLM via Amsterdam.