Leardriver,
The Lindz Four IS an obstacle departure. You're asking about the departure proceedure (DP) published on the back of the 13-1 plate in the takeoff data section below the airport diagram. This departure is the same as the Lindz; read the text and compare it.
If you can't meet the climb gradient, should you really be departing? This is something to think about before you fly to that airport, not before you leave.
Former SID's and obstacle departures are all combined now as Departure Proceedures. You'll note that a comparison between the climb gradient depicted in the takeoff data for ASE, and the Lindz Four, shows that the required gradient is the SAME.
Under IFR, the PIC is responsible for terrain and obstruction clearance until this responsibility is assumed by ATC in the form of radar vectors. A VMC departure may allow for terrain clearance by maneuvering, but may not take into account the ability to maneuver in a like manner with the failure of a powerplant. Under Part 91 this isn't an issue unless something goes wrong. At such point compliance with 91.13 and 91.103 will be considered. Under 121 or 135, the climb gradient must be met and the proceedure flown.
TERPS criteria, upon which the DP is predicated, provide for terrain and obstacle clearance. Should you elect to provide your own, you may at some point be required to show how you determined this. In the case of a clear visual departure, this is a matter of showing that you saw the rocks and went around them. This can be done under Part 91. For operations under Part 135 or 121, the operator must show an alternate means of compliance. Failing an exhaustive study of clearance criteria, as provided for in TERPS, an operator may have a hard time making a case for an IMC departure without full adherence to the DP. Further, as it's already published, there is no reason not to use that proceedure.
If the climb gradient cannot be met with all engines turning, seriously consider altering your flight operation. This may mean making an extra trip, removing fuel, leaving baggage, or whatever must be done in order to make a safe and legal departure. If the gradient cannot be met on two or more engines, it can't be met on less. This presents a dillema during a power loss. In the case of ASE, referring to the named DP won't excuse you from climb gradient requirmements any more than referring to the text description on the takeoff minimums data section will relieve you from those of the named DP (Lindz). Six of one, half dozen the other, and the hills haven't moved. You still must clear them.
See the excerpt from FAA Order 8400.10 copied below.
FAA Order 8400.10, Vol 4, Ch 3, Sec 1, para 927E:
E. Takeoff Minimums. TERPS criteria is based on the assumption that the airplane can climb at 200 feet per nautical mile (approximately 30:1) to the minimum enroute altitude through the takeoff flightpath.
(1) When obstacles penetrate the obstacle clearance plane, the airplane must be able to climb at a steeper gradient or to use higher than standard takeoff minimums to allow the obstructions to be seen and avoided under visual conditions. Authorizations for lower than standard takeoff minimums are based on the operator adjusting airplane takeoff weight to avoid obstacles in the takeoff flightpath if an engine fails on takeoff. POIs shall not authorize operators who do not prepare an airport analysis and perform obstacle climb computations to use lower than standard takeoff minimums. POIs may approve a system in which the operator makes obstacle clearance computations and performs lower than standard visibility takeoffs on specified runways, as opposed to all runways.
(2) The criteria for TERPS does not take into account whether or not the aircraft is operating on all engines. Operators must either show compliance with TERPS criteria with an engine out or have an alternate routing available for use in case of an engine failure. Specific guidance for approval of these procedures is in development and will be included in this handbook at a later date.