[SWHouston]

My Male Sneakers is the resident, has tenure as Oliver does, and any Dog you bring in, should be encouraged to take second place. Some don't agree, but, there is/should be a pecking order, and when it's established, things work very well. Having an Alpha and subordinates, is a natural condition when establishing a Pack, which is what you are doing.

YOU, need to make sure that Lucy completely understands that you support Olivers place as the Alpha. You might try the following...

Greet Oliver first when returning home,
Pet him more/more vigorously than Lucy.
Feed him first, specially when handing out treats.
Allow Oliver "lap" time, while Lucy watches from a distance.
When Oliver "corrects" (snaps/growls) at Lucy, it's Lucy's fault, and she should be "corrected", NOT Oliver.
Do not take Lucy aside (behind Oliver's back), and try to make up for the presumed neglect, that will only reinforce her aggression in this instance, and prolong establishing of the Pack.
If you allow "them" to sleep with you, give Oliver a preferred place on your Bed, possibly make Lucy sleep on the floor.
When walking/jogging, allow Oliver to walk beside you, or take point, while Lucy walks behind him. Adjust Leash length to control this.

I know this sounds rather tough, and many can't pull this off...

Can you ?