From what you've said at least one of the LH relays are working. One of the relays powers the 'system', including the fuel injectors. If you have +BAT going to the orange wire on the injector with the ignition on (which you do) the power has made it through the ignition key, the 25A fuse and one of the dual relays (that the LH computer has activated).

The hot contact of the second relay, the fuel pump relay, get its power from the output of the system relay. The fuel pump relay coil is driven directly by the LH computer. When the ignition is first turned on, the LH immediately activates the fuel pump relay to prime the fuel system. If no engine pulses have been seen in any 3 second period (therefore the engine flywheel is not turning), the LH deactivates the relay as a safety precaution. You are getting proper crank pulses from the ignition computer since you say the engine will eventually run, so that is not the problem.

Take the cover off the dual relay and observe what happens when you turn the ignition on. Both relays should come, and one will drop out after the 3 second timeout. If they do, it sounds like the LH computer is doing its job and the problem rests in the relay itself or the wiring from the relay to the pump.

If one never comes on, try activating that relay contact manually; the pump SHOULD RUN. If it runs that means the relay contacts, the power feed from the system relay and the wiring from the pump are all intact. If the pump still doesn't run, the only questions remaining would be the power feed from the system relay, the relay coil itself or the relay driver in the LH.

BTW - don't getted too comfortable driving around with a hotwired fuel pump!

Cheers.