The word Ligne is old French origin and was used as a length measurement
The description 'Line lamp' is of German origin Line correct spelling Ligne sometimes written "' indicates the Brightness of the Lamp, this can also be expressed as Candle Power [CP], Watts, [w] Lumen's [LU] and other words chosen by Eurocrats.
The Brightness of a Lamp depends on a lot of factors, Fuel & Wick quality, Air Flow, Chimney Heights and Diameters, Atmospheric pressure and quality, sometimes sheer perversity.
A 20"' lamp with a circular wick is about 50 Candle power
Describing a Lamp as a 12 or 14 line lamp has the added benefit of capturing the customer into buying 20 or 30 line wicks, stamped with the Manufacturers Name and the Line Value
.Some Line Lamps require Tubular Wicks, if yours is one of these you may need to contact me, others are Standard Flat Wicks in a Kosmos or Matador Burner which turns them into a tube formation.
CAUTION The line rating of the wick has no bearing on the Chimney size
Take the wick out lay it flat and measure the width in inches then go to flat lamp wicks and select the nearest,
1/16 - 1mm of an inch under can be forgiven., but not over
English Kosmos ( also modern imported Repro) Flat wicks 6"' 1-3/8 8"' 1-5/8 10"' 1-15/16
12"' 2-1/4 14"' 2-5/8
Imported DHR Lamps
Pantry Lamp - Large Table Lamp - French Ceramic Base Lamps all use 2-1/2" flat wicks
Small Table lamp - Trawler Lamp - Engine Room Light all use 1/38" Flat wicks