I personally do not think it is a Linsley Brothers cartridge. I checked back through the cartridge name lists I have and no mention is made of the brand name Rapid being associated with Linsley. Also I have never seen limited abbreviated to just an “L”. Another point worthy of note is that of all the cartridges and information I have on them they are always referred to as Linsley Brothers, never Linsley Brothers Limited, to me that pretty much rules out it being short for “Limited”. As for it standing for Leeds I somehow doubt it, never seen Leeds substituted to just an “L”.
Added a few known Linsley Head Stamps, as can be seen the name and city are always spelt in full with just the brothers being shortened to Bros.
Hard call but I have asked others and got back a bland “no”. So unless somebody turns up a box with some more information on I guess we won’t know for sure.