The Lumbridge mine, also called the caved-in mine, was released during the Learning the Ropes quest update. It no longer exists due to an update of Jagex, the tutorial being replaced by Unstable Foundations. It contains tin and copper ore, and 3 anvils. The smithing tutor and mining tutor are found here. Unfortunately, after the tutorial, the mine caves in, though the tutors residing within had escaped. It is revealed later that the cave-in was caused by a three-headed Dragon, which had escaped a fight with Sir Vant underneath Lumbridge.
The mine was most likely under River Lum, as there is a small pool in it with water constantly dripping in. There were mining cart tracks there leading into unknown places. Also, after the update, a large chunk of rock appeared in Lumbridge, possibly part of the mine.