(defun random-permutation (the-list)
	(cond
		((null the-list)
			()
		)
		(T
			(setf temp (nth (random (length the-list)) the-list))
			(cons  temp (random-permutation (take-from temp the-list)))
		)
	)
)

Demo:


[24]> (random-permutation ())
1. Trace: (RANDOM-PERMUTATION 'NIL)
1. Trace: RANDOM-PERMUTATION ==> NIL
NIL

[35]> (random-permutation '(1 2 3 4))
1. Trace: (RANDOM-PERMUTATION '(1 2 3 4))
2. Trace: (RANDOM-PERMUTATION '(1 2 3))
3. Trace: (RANDOM-PERMUTATION '(1 2))
4. Trace: (RANDOM-PERMUTATION '(2))
5. Trace: (RANDOM-PERMUTATION 'NIL)
5. Trace: RANDOM-PERMUTATION ==> NIL
4. Trace: RANDOM-PERMUTATION ==> (2)
3. Trace: RANDOM-PERMUTATION ==> (1 2)
2. Trace: RANDOM-PERMUTATION ==> (3 1 2)
1. Trace: RANDOM-PERMUTATION ==> (4 3 1 2)
(4 3 1 2)

[39]> (random-permutation '(2 22 222))
1. Trace: (RANDOM-PERMUTATION '(2 22 222))
2. Trace: (RANDOM-PERMUTATION '(2 222))
3. Trace: (RANDOM-PERMUTATION '(222))
4. Trace: (RANDOM-PERMUTATION 'NIL)
4. Trace: RANDOM-PERMUTATION ==> NIL
3. Trace: RANDOM-PERMUTATION ==> (222)
2. Trace: RANDOM-PERMUTATION ==> (2 222)
1. Trace: RANDOM-PERMUTATION ==> (22 2 222)
(22 2 222)
[40]> (random-permutation '(a b c d))
1. Trace: (RANDOM-PERMUTATION '(A B C D))
2. Trace: (RANDOM-PERMUTATION '(A B D))
3. Trace: (RANDOM-PERMUTATION '(A D))
4. Trace: (RANDOM-PERMUTATION '(D))
5. Trace: (RANDOM-PERMUTATION 'NIL)
5. Trace: RANDOM-PERMUTATION ==> NIL
4. Trace: RANDOM-PERMUTATION ==> (D)
3. Trace: RANDOM-PERMUTATION ==> (A D)
2. Trace: RANDOM-PERMUTATION ==> (B A D)
1. Trace: RANDOM-PERMUTATION ==> (C B A D)
(C B A D)
[41]> (random-permutation '(1 2 sdf 335 t3))
1. Trace: (RANDOM-PERMUTATION '(1 2 SDF 335 T3))
2. Trace: (RANDOM-PERMUTATION '(1 2 335 T3))
3. Trace: (RANDOM-PERMUTATION '(1 2 335))
4. Trace: (RANDOM-PERMUTATION '(1 2))
5. Trace: (RANDOM-PERMUTATION '(1))
6. Trace: (RANDOM-PERMUTATION 'NIL)
6. Trace: RANDOM-PERMUTATION ==> NIL
5. Trace: RANDOM-PERMUTATION ==> (1)
4. Trace: RANDOM-PERMUTATION ==> (2 1)
3. Trace: RANDOM-PERMUTATION ==> (335 2 1)
2. Trace: RANDOM-PERMUTATION ==> (T3 335 2 1)
1. Trace: RANDOM-PERMUTATION ==> (SDF T3 335 2 1)
(SDF T3 335 2 1)