Sorting by checking 2 distance away elements in a list, and check the method's accuracy
With python 2.7, you have xrange. The improvement in performance might be minimal (but an improvement nonetheless):


  The advantage of xrange() over range() is minimal (since
  xrange() still has to create the values when asked for them) except
  when a very large range is used on a memory-starved machine or when
  all of the range’s elements are never used (such as when the loop is
  usually terminated with break).




Split your \$ L \$ and use map as soon as possible.

L.append(map(int, raw_input().split()))




Swapping in python is as easy as:

a, b = b, a


No need to allocate a temporary dummy (and del it later):

if l[index] &gt; l[index + 2]:
    repeat = True
    l[index], l[index + 2] = l[index + 2], l[index]




Now, for the time limit issue, since you know that you are actually sorting the even and odd indexes sublists disjointly; splice your \$ L \$ and sort those. Then, reattach them both by weaving them together.

# L has been read from user
l_even = sorted(l[::2])
l_odd = sorted(l[1::2])


and then join them together.