Short answer: Library Live Sets must be installed as part of a Library save file (X7L).

Longer: There are 3 primary areas of memory on Montage and each is different in the freedom to write/change this memory. The three memory areas are Presets, Library, and User.

Presets are the most restricted in terms of ability to write/change this memory. There is only one operation that can change the presets - the firmware upgrade. During a firmware upgrade, if any change is made to Presets then typically only new Performances will be added. Other than a firmware upgrade - which is a relatively rare occurrence - there is no way for you to modify, change, overwrite, or delete presets. These are set only by Yamaha and the user has no control over this area other than the choice to update or not update firmware. The Preset area does have a live set associated with it (the Preset bank within Live Set). None of this information can be changed or modified since it is saved within the Preset memory area which follows the write/modify rules previously outlined.

The Library memory is highly related to the preset memory. The Library area has 8 slots that are initially empty with no libraries installed. Once a library is installed, like the Preset area, you cannot modify or change the information in the Library slot. Unlike the Preset area - the Library area can be modified and manipulated by more than just a firmware upgrade. At any time, you can either erase/delete an installed library or you can install a library into an open library slot (assuming one out of the 8 is empty). Installing a Library must be done where all Performances (and Live Set) within that Library is installed at once. You cannot write individual Performances one-by-one into the Library area. The Library slot must be installed in one fell swoop. There are only two operations to install a library: the library "load" operation and also loading a supported legacy file (like Motif XF) and choosing the Library area as the target. Note that converting legacy files will not contain any Live Set information since legacy products did not themselves have Live Sets. Once you install a Library, there is no way to modify any of the contents within the Library. It is, like presets, "read only" except that you can delete an entire Library slot to start over or clear a space for another Library slot.

User memory is the only area where you are free to modify the contents one item at a time. You can modify any Performance and overwrite a single Performance or you can change and reorder the Live Set area. Your User area is the only bank which allows for freely editing items. Therefore, without using external software, this is the only mechanism and area for you to change Live Set contents. If you want to access/change the Live Set within a Library - you must first import the library into the user area then create the Live Set inside the user area. Save both a user file and a library file. Saving the user file allows for you to more easily load your Live Set into the user area later if you need to change it.

Unfortunately, I'm not aware of any operation that will import the Live Set from a Library slot to the User area or to load a Library directly to the User area such that you can modify the Live Set contents of a Library file.

The John Melas Tools allow you to recreate your own libraries and live sets and resave for a more customized experience. Check out John's video from Superbooth last year to see it in action.

John Melas tools are nice, but a bit on the expensive side. It would be nice if Yamaha grows their "Connect" app to incorporate similar functionality.

I did not mention JM tools because the OP states:

directly from the MONTAGE

Which precludes external software - even including Montage Connect or free software. It's good to know what's available on that front - but also important to know which hoops to jump through using the instrument alone.

I personally do not own the JM tools - so I live in a space of levering the instrument more than software tools. Sometimes I write my own tools - but this is outside of scope of being helpful to anyone else. Primarily to gather statistics like the extended Performance listing ("cheat sheet" ) or the online X7U / X7L analyzer which spits out performance names and waveforms as this was something some user was needing to offline view the contents of their save files.

Is there a way to access the Llibrary Live Sets ( 9 - 16 ) directly from the MONTAGE. Or do they only appear if they are installed together with a library

Live Sets (are very misunderstood). It is a Set List.

The Preset Live Sets refer to the Preset Banks.
A Library Live Set refers to the Performances in that Library Bank.
The User Live Set area is where you, the User, can take any Performance and put it on your “set list”.

There can be only one Live Set active at a time.
Live Sets reference, “point to”, a Performance location. If you Delete the original Performance from its location, the Live Set slot will read “Not Found”. They are not entities on their own. They count on the original data being in a specific location. They “point to” the original Performance in the location you created it from...

You recall a Performance... you hold [SHIFT] + [LIVE SET] to ‘register’ the Performance on the list... if you remove (Delete) the original then the Live Set slot is “Not Found”.

There can be only one Live Set active at a time. Can’t be stated enough...
A list can contain 256 slots. In the User Live Set area you can have 8 lists of 256 slots... that's 2048 slots total.
When we say 256 Slots, this means if you have a FS set to "LIVE SET+" you can advance through 256 programs.
A User Live Set becomes a Library Live Set when you SAVE the current User data as File Type = Library File then install it to one of eight Library locations.

There can be only one Live Set active at a time. Can’t be stated enough...

And unfortunately that is one of the biggest weak spot of the MONTAGE. Can’t be stated enough...

And unfortunately that is one of the biggest weak spot of the MONTAGE. Can’t be stated enough...

What a silly statement!
You have 8 User Banks of Live Sets each with 256 list slots.
You have 8 Live Set Banks available within each Library.
That’s 72 Set lists, each with 256 slots each

Only one List can be active at a time. What don’t you get?