The earth is cracking and molten earth is "escaping" every day. We call this process rifting and it is occurring at the bottom of the Pacific and Atlantic Oceans, including right through the very center of Iceland. Molten lava also "seeps" out of volcanoes--for example, there is lava flowing right now in Hawaii. Because of the density of lava, it can't leave the atmosphere--just like you and I can jump in the air, but we always land back on the surface of the Earth, lava can be spout like a fountain from a volcano, but it always lands on the surface of the Earth.

If we were able to create a container that could hold molten lava and transport it into space, it would definitely cool (we'd call it quench) and it would orbit around our planet.

How would it 'seep into space'?Do you mean it escapes Earth's gravity?

It would not remain liquid in a vacuum. The lava would either boil or it would freeze, simply because liquids cannot exist in a vacuum. That said, all of the trapped gas inside of the lava would come out as gas, so the lava would make its own atmosphere.