There's a few ways of doing this, and the correct method depends on the type of cover you want to use in place of the knackered ones. To avoid overcomplicating things (hopefully) I'll split the cover types into two categories - those that sit inside a Crown Unit and those that are directly bedded.
The Crown Unit is the concrete 'frame' that carries the concrete 'lid'. You've reported that these are broken, which usually indicates that they were never properly installed. Many crown units offer the opportunity to replace the standard concrete 'lid' with a shallow steel cover that simply sits inside the the 'frame'. These are only suitable for light-duty residential driveways and, to my way of thinking, if you've got to replace the broken stuff, you might as well make a decent job of it and go with a medium duty cover (Class B or above).
The stronger replacement covers tend to be thicker, 100 or 150mm thick in most cases (although there are some ductile iron Class B covers that are 40/50mm thick) and thse need to be directly bedded onto supporting masonry and then have the paving patched in around them. The exact detail of the support masonry depends on the type of cover you choose, but will, more than likely, consist of 225mm brickwork or 150mm concrete seating rings, with the new frame mortar-bedded onto the masonry. To accommodate the cover and the support masonry, it might be necessary to remove one of the chamber sections (what you call the 'liner') to 'make room' for the deeper cover and it's masonry.
The best way to proceed is to choose your new covers. You could try the
Manhole Covers website or your local Contractors Merchant to see what suits your taste and your pocket, not to mention the type of paving you have at the moment. Will a simple 450x600 Ductile Iron cover be ok, or would you prefer a
recess tray?
If you give me a better description of the current layout, including the type of paving, then I should be able to suggest a 'best way forward'.