Algol,
Probably the easiest reference for terrain in that area is the 33 LOC chart.
That chart has an 11 DME point marked on the chart, which makes the comparison easy. Abeam the 11 DME point there is a spot height of 3602 ft and a little further to the north west is a spot height of 4289 ft.
11 DME is by my calculation about 8.4 nm from the end of the runway.
Minimum gross climb gradient for a twin on one engine is 2.4% (1.6% nett). 2.4% is about 144 ft/nm give or take a few feet.
If the aeroplane is climbing at 2.4% then in the 8.4 nm it covered to get to 11 DME it will have climbed about 1200 ft.
Now it will only be doing that if a number of planets align, but it is not inconceivable that the aeroplane loaded to max performance limiting take off weight would only be maybe 1200-1300 ft at around 11 DME.
This is why a lot of operators do the departure end of the runway turn and get the aeroplane away from the terrain and over the water.
To clarify one thing though, even though LIDO provide this info via their EFB, it isn't "LIDO approved" they are just the messenger.
I think you are right to question the procedure.