Implement the "Lazy Sort"
Jelly, &nbsp;14 12 11&nbsp; 9 bytes

-2 bytes thanks to ETHproductions (use the minimum dyad, «)

I’«0Ṛ+\Ṛ+


A monadic link taking and returning lists of integers.

Try it online! or see the test suite.

I really don't think this is Lazy™ enough!

How?

I’«0Ṛ+\Ṛ+ - Link: list of integers, a              e.g. [ 8, 3, 3, 4, 6, 2]
I         - increments between consecutive items of a   [-5, 0, 1, 2,-4 ]
 ’        - decrement (vectorises)                      [-6,-1, 0, 1,-5 ]
   0      - literal 0
  «       - minimum of decremented increments and zero  [-6,-1, 0, 0,-5 ]
    Ṛ     - reverse                                     [-5, 0, 0,-1,-6 ]
      \   - cumulative reduce with:
     +    -   addition                                  [-5,-5,-5,-6,-12]
       Ṛ  - reverse                                     [-12,-6,-5,-5,-5]
        + - addition (with a)                           [-4,-3,-2,-1, 1, 2]