There is a large number of Harrison manuals at the 'usinages' site:
https://passion-usinages.forumgratuit.org/f32p100-tours-lathes
(this link may not be the correct page – they are listed in alphabetical order and Harrison starts on page 3 of 8 on my browser).
I do not know if the L5 one has the TT attachment in it, but you could also try the L6 and 140 one.
I can only speak for Colchester TT attachments and they do use a different leadscrew (longer and splined at the handle end). Can you partly dismantle your own lathe and see if they are identical or different to what you have?