The cyclist and Hudson have refused to comment on their relationship, despite much media speculation that they are a couple.
Armstrong met Horn at the Ivy At The Shore in Santa Monica on Tuesday. They ate their meal on a patio at the back of the restaurant to avoid the paparazzi.
"They were having a great time and enjoying each other's company," a source told People. "Goldie was all smiles. Lance was sitting next to her and they were chatting while Kate was laughing.
"They were all just really happy."