It IS your programme and part M requires you to have a copy of it and to fully undestand it. It will have your name on it, and at some time you will have signed it to say that you are responsible for the maintenance of your aircraft. You are also able to sub contract that responsibility to an approved organisation.
However the programme you signed (LAMP) is deemed by EASA to be not suited for purpose.
Someone (your CAMO or yourself) will have to obtain an EASA approved type specific and equipment specific programme. These as I have indicated above have long been available in France for all certified aircraft registered in France.
Rather than search for non existant manufacturers programmes (particularly for American or British aircraft) why not obtain the already developed and up to date French programme?
The cost of this should be laid at the doors of the CAA who decided to hang on to the generic LAMS/LAMP; at least they ought to fund the translation costs from French to English.
It is barking mad to try to develop from scratch a new type specifc programme when all the work has already been done by the French.
Two ways we might get a programme?
1. The CAA make an official request to the DGAC/OSAC for access to their files, and make the programmes available (for a fee!)to the UK GA fleet. We (the UK GA owners) personalise the programmes by putting our names on each page and signing the declaration of responsibility. We also acknowledge that only the French original has authority (unless we get a CAA approved translation) and our English translations are for info only. We then submit the personalised programmes back to the CAA for approval and pay them yet another fee.
2. Those of us who regularly fly to France ask the French owners of similar aircraft to e-mail a copy of their approved programme to us. We then get someone (

nice little earner!) to do an English translation. The two programmes English & French are signed and personalised and submitted to the CAA for approval.