Inspired by a recent trip along St Cuthbert's Way, and a question I asked Hamish Brown at a talk he gave recently (I asked "what is your favourite LDP in Britain?" and he answered, "the best one is the one you make up for yourself.") I imagined a route not from Melrose to Lindisfarne, but all the way from Iona, a tribute to the Ionan monks who founded the Lindisfarne monastery, a grand pilgrimage across the width of Scotland.
The more I thought about this route, the more excited I got about the high quality of both the scenery passed through and the walking, much of it on established paths and trails.
Iona Beach:
It's map time. If you have them, get OS Landrangers 48,49,50,56,64,72,73,74,75 out. Now imagine a route like this. Spend the night on Iona, exploring the island and monastery, visiting the bay at the back of the ocean and climbing Dun I.
Dun I view towards Mull:
Next day, get the ferry to Fionphort and walk past the tidal island of Erraid to the amazing sands of Traigh Geal, the best beach on Mull.
Sound of Iona near Erraid:
Accomodation might be difficult on the next stretch, a long and involved but high quality two-day walk along the southern shore of the Ross of Mull, either visiting the Carsaig Arches, or keeping to the clifftop high above and descending to Carsaig at the Nun's Pass, before further shoreline walking to Lochbuie and Moy Castle.
Carsaig arch:

After Moy, walk inland to Mull's longest glen, then over the Corbett of Dun da Gaoithe and down to the ferry and facilites at Craignure.
Oban ferry and Duart Castle:

Refresh in Oban, gateway to the islands, before taking backroads and paths to Loch Nant (or via Deadh Choimhead - there's no obvious single route out of Oban) and swing north for Taynuilt.
Loch Nant (©Patrick Mackie, geograph):
Beyond Taynuilt, take to the SE shore of Loch Etive, where two options appear. The finer, longer, but more off-route trail leads into remote Glen Kinglass and the beautiful country around Loch Dochart, before picking up the West Highland Way at Inveroran.
Loch Etive north of Taynuilt:
Alternatively, head into Glen Noe, down to Stronmilchan near Kilchurn Castle, a short road tramp, then forest/hydro trails and a short boggy moorland section south of Ben Lui to meet the West Highland Way at Inverarnan.
Loch Lomond near Inverarnan:
Then it is the West Highland Way then Kelvin Way all the way in to Glasgow.
On Kelvin Way, Glasgow West End:
Glasgow can either be enjoyed as a stop in itself, visiting the Scottish mainland's only undamaged pre-Reformation cathedral, or scurried through, picking up the Clyde Walkway all the way to Lanark and the Falls of Clyde.
Falls of Clyde, New Lanark:
I'm not sure exactly how the route would then go - perhaps over Tinto and a little bit of road walking - before picking up the John Buchan Way from Broughton to Peebles.
Tinto from Broughton Heights:
A pleasant walk along the Tweed to Innerleithen, then onto the hills again over Minch Moor on the Southern Upland Way to Melrose.
Melrose Abbey:
Finally, the 62 miles of the St Cuthberts Way over the Cheviots to Lindisfarne, waiting for low tide, to cross barefoot to Holy Island.
Lindisfarne sands:
This isn't the only possible route. Certainly the coastal approach to Lindisfarne from Berwick is very fine, and the Tweed is a good river for walking along. The whole thing would be around 280 miles and likely take around two and a half weeks to walk.
As I currently don't go on long walks, I like to imagine them... where would your pilgrimage be?