Lift braking device for braking a lift cage on a braking web, preferably a braking web integrated in a guide rail, the lift braking device (20, 20') including: - a brake housing, - a first brake body, which is arranged at the brake housing to be movable and which is constructed to be moved with the braking web when contact with the braking web and relative movement between braking web and brake housing take place and thereby to clamp the braking web and strain the brake housing, and - a presser, which is arranged at the brake housing so that the braking web can be arranged between the first brake body and the presser, - wherein in a normal setting there is a spacing between the first brake body and the presser at least corresponding with the thickness of the braking web plus a required passage tolerance between the brake body, the braking web and the presser, - wherein the presser when required is adjustable in the direction of the first brake body substantially along a line of action extending perpendicularly to the braking web and the presser can be pressed against the braking web able to be arranged between the first brake body and the presser, characterised in that - the first brake body can be brought into contact with the braking web by a counterforce acting on the braking web due to the pressing of the presser, - wherein the lift braking device (20, 20') further includes a pressing lever, which is pivotably mounted at the brake housing and which when required acts on the presser in order to press this against the braking web to thereby laterally displace the brake housing and to bring the first brake body into contact with the braking web. - a brake housing, - a first brake body, which is arranged at the brake housing to be movable and which is constructed to be moved with the braking web when contact with the braking web and relative movement between braking web and brake housing take place and thereby to clamp the braking web and strain the brake housing, and - a presser, which is arranged at the brake housing so that the braking web can be arranged between the first brake body and the presser, - wherein in a normal setting there is a spacing between the first brake body and the presser at least corresponding with the thickness of the braking web plus a required passage tolerance between the brake body, the braking web and the presser, - wherein the presser when required is adjustable in the direction of the first brake body substantially along a line of action extending perpendicularly to the braking web and the presser can be pressed against the braking web able to be arranged between the first brake body and the presser, characterised in that - the first brake body can be brought into contact with the braking web by a counterforce acting on the braking web due to the pressing of the presser, - wherein the lift braking device (20, 20') further includes a pressing lever, which is pivotably mounted at the brake housing and which when required acts on the presser in order to press this against the braking web to thereby laterally displace the brake housing and to bring the first brake body into contact with the braking web. - wherein in a normal setting there is a spacing between the first brake body and the presser at least corresponding with the thickness of the braking web plus a required passage tolerance between the brake body, the braking web and the presser, - wherein the presser when required is adjustable in the direction of the first brake body substantially along a line of action extending perpendicularly to the braking web and the presser can be pressed against the braking web able to be arranged between the first brake body and the presser, characterised in that - the first brake body can be brought into contact with the braking web by a counterforce acting on the braking web due to the pressing of the presser, - wherein the lift braking device (20, 20') further includes a pressing lever, which is pivotably mounted at the brake housing and which when required acts on the presser in order to press this against the braking web to thereby laterally displace the brake housing and to bring the first brake body into contact with the braking web.