A luted line is a line with a lute in it. A lute is 'U' tube configuration within a pipework section which, when filled with liquid, acts as a seal and prevents gas flow in the pipework.
In a distillation column, vapour from the top of the column passes to the condenser where at least some of it is condensed. A portion of that condensed is returned to the top of the column as reflux. The pressure at the top of the column is greater than at the condenser outlet caused by the frictional resistance to vapour flow in the pipework and in the condenser.
A classic use of a lute is to be found in the gravity reflux line between a distillation column and its condenser. Liquid condensate (reflux)can flow from condenser to column by gravity, but vapour is prevented from flowing in the reflux line in the reverse direction, even though the pressure at the column is greater than the condenser, by the action of the lute.
The depth of the lute determines the maximum pressure difference at which the seal can operate. At any greater pressure difference, the lute "blows" and the gas forces the liquid, piston-like, out of the lute.
In the above example of a lute position, one must ensure that the depth of the lute expressed as head fluid flowing is always greater than the maximum vapour pressure drop between column top and condenser outlet.