However when someone else cast a doubt and a worry was, in case of an engine failure and a single engine initial climb after lift off, would the aircraft still be able to comply with the minimum gradient requirement and obstacle clearance, in that case of delayed rotation, or even a "worst case", rotating near the end of the runway?
In general, yes, and would be safer (able to climb out faster/steeper) actually.
Delayed rotation means that you will have a higher speed on the climb out which means you'll be able to have a higher climb rate/gradient meaning better obstacle clearance.
But FAR 25 and CAR 525 don't specifically deal with 'obstacle clearance'. They deal with
aircraft performance. To ensure obstacle clearance, if you're IFR, you must follow the appropriate procedures. The standard departure is 1/2 statute mile visibility and has the following conditions: cross the departure end of the runway at 35', climb at 200'/NM until you reach your enroute altitude and maintain runway heading until 400' AAE. Those procedures are based on the obstacle clearance requirements that are part of the US TERPS, TC TP-308, and ICAO documents. The standard Obstacle Clearance Surface that applies to the standard 1/2 mile departure is a 40:1 slope. 40:1 = 152' of vertical climb for every 1 nautical mile. No obstacle are to penetrate that OCS for a standard departure, ie: a 200'/NM climb gradient. That provides at least 48'/NM of clearance from all obstacles. As long as you abide by the instrument departure procedure for the runway you're using, you will be guaranteed obstacle clearance.
Also, regarding OEI climb performance, the obstacle clearance requirements do not change. Depending on what part of FAR or CAR you're operating under, you may or may not need to ensure compliance with the instrument departure procedure assuming OEI. But either way, I can ensure you that just because the regulations say you don't need to ensure obstacle clearance with OEI, you NEED to ensure OEI obstacle clearance - the obstacles don't just disappear when you lose an engine, they will be waiting for you if you decide to go below the appropriate altitude!