Each Alliance handles the subject of purely domestic lounge access differently, particularly when it comes to US program status holders: Status-based lounge access is generally restricted to the airport(s) you are departing from.

oneWorld: American/Alaska status holders are precluded from OW lounge access on purely domestic itineraries. Other program Sapphire/Emerald holders do enjoy Business/First class lounge access on domestic itineraries..

Star Alliance: United Star Gold members are precluded from status-based access to the United Club on purely domestic itineraries. United Star Gold members can access other lounges operated by a Star-Alliance member (not a contract lounge) on domestic itineraries. Other Star Gold members also have access to the United Club.

SkyTeam: No status-based access to anyone on purely domestic itineraries.

So as it applies to you:

IAH: United flight from IAH > LAX. I have United Premier Gold/Star Alliance Gold: No access in IAH as the only *A operated lounged are United Clubs.

LAX: Delta flight from LAX > DFW. I have Flying Blue Gold/SkyTeam Elite Plus. No access in LAX as SkyTeam does not require status-based domestic lounge access for any holders.
LAX: United flight from LAX > SFO. I have United Premier Gold/Star Alliance Gold. You would have access to the Star-Alliance business class lounge in the Tom Bradley International Terminal. You would also have access to the Air Canada Maple Leaf Lounge at LAX (currently closed). No access in SFO unless you are continuing onto another destination on United/Star Alliance.
LAX: Alaska flight from LAX > SFO. I have Alaska MVP Gold/Oneworld Sapphire. No access as oneWorld does not mandate access to AA/AS status holders on purely domestic itineraries.