Intermittant power

What makes you say there was no power in the outlet? Did you use a voltmeter to verify?

What I'd think of off the top of my head is a loose or intermittently bad ground inside the outlet.

Also, I'd try that lamp in another outlet and see how it works there.

As Rag says, Bri, it sounds like a loose connection. A loose ground is especially risky because voltage can be present on a fixture apparently off

It certainly does sound like a loose connection, but it won't be the ground. Test the outlet that isn't working from the neutral to ground using an ohmmeter to see if there is continuity (multi-meters have this function). If there is continuity, then your power wire (the black) has a bad connection. If there is no continuity, then your the neutral (white) wire has a bad connection. First check the connections at the device boxes that aren't working, and if everything appears good, then check the device (switch and outlet) boxes of working devices where they may get power from. It's always a safe idea to power down branch circuits BEFORE removing the devices to inspect them. The test above assumes you have a connected and working ground wire.