A lock cylinder comprising a cylinder housing; a disk housing rotatably supported about a cylinder axis in the cylinder housing; and a plurality of rotatably supported disk tumblers arranged along the cylinder axis in the disk housing, wherein each disk tumbler has a reception opening for a key, a blocking cut-out at the outer periphery for an at least partial reception of a blocking pin aligned in parallel with the cylinder axis and, offset from the blocking cut-out, a fixing cut-out provided at the outer periphery for an at least partial reception of a core pin aligned in parallel with the cylinder axis; wherein the disk tumblers are rotatable from a starting position with a removed key by a rotation of the introduced key in an unlatching direction into an end sorting position in which the blocking cut-outs of all the disk tumblers are oriented in alignment with one another, viewed in the direction of the cylinder axis; wherein, in the end sorting position, the fixing cut-outs of all the disk tumblers are oriented in alignment with one another, viewed in the direction of the cylinder axis, with the lock cylinder being adapted such that, on a further rotation of the disk tumblers out of the end sorting position in the unlatching direction, the core pin first engages into the fixing cut-outs and the blocking pin only then engages into the blocking cut-outs; and wherein at least one lift disk is provided which is arranged in parallel with the disk tumblers and which is rotatably supported in the disk housing and which has a reception opening for the key, with the lift disk being compulsorily coupled with the introduced key with respect to a rotation of the key, characterized in that a control element which is separate from the blocking pin and which is independently movable is associated with the lift disk and is supported in a slit of the disk housing, with the lift disk having a cut-out at its outer periphery for a partial reception of the control element, and with the lift disk being able to be selectively fixed at the disk housing by engagement of the control element into the cut-out so that the lift disk and the disk housing can only be rotated together. a cylinder housing; a disk housing rotatably supported about a cylinder axis in the cylinder housing; and a plurality of rotatably supported disk tumblers arranged along the cylinder axis in the disk housing, wherein each disk tumbler has a reception opening for a key, a blocking cut-out at the outer periphery for an at least partial reception of a blocking pin aligned in parallel with the cylinder axis and, offset from the blocking cut-out, a fixing cut-out provided at the outer periphery for an at least partial reception of a core pin aligned in parallel with the cylinder axis; wherein the disk tumblers are rotatable from a starting position with a removed key by a rotation of the introduced key in an unlatching direction into an end sorting position in which the blocking cut-outs of all the disk tumblers are oriented in alignment with one another, viewed in the direction of the cylinder axis; wherein, in the end sorting position, the fixing cut-outs of all the disk tumblers are oriented in alignment with one another, viewed in the direction of the cylinder axis, with the lock cylinder being adapted such that, on a further rotation of the disk tumblers out of the end sorting position in the unlatching direction, the core pin first engages into the fixing cut-outs and the blocking pin only then engages into the blocking cut-outs; and wherein at least one lift disk is provided which is arranged in parallel with the disk tumblers and which is rotatably supported in the disk housing and which has a reception opening for the key, with the lift disk being compulsorily coupled with the introduced key with respect to a rotation of the key,