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No need for L2. With your definitions :

sage: list(map(F, L0, L1))
[0, 1, 2, 3]

From map?

map(func, >>*<<iterables) --=""> map object

Make an iterator that computes the function using arguments from each
of the iterables.  Stops when the shortest iterable is exhausted.

Learn Python !

No need for L2. With your definitions Two possibilities (among others I suppose...) :

sage: list(map(F, L0, L1))
[F(u[0], u[1]) for u in L2]
[0, -3, -6, -9, -2, 1, 1, -2, -8, -1, 2, 5, -18, -7, 0, 3]
sage: list(map(lambda u:F(*u), L2))
[0, -3, -6, -9, -2, 1, 1, -2, -8, -1, 2, 5, -18, -7, 0, 3]`

Building `L2 isn't necessary :

sage: [F(*u) for u in Set(L0).cartesian_product(Set(L1))]
[0, -2, -8, -18, -3, 1, -1, -7, -6, 1, 2, 0, -9, -2, 5, 3]

From I suppose that the map?itertools standard Pythonlibrary offers other possibilities...

Make an iterator that computes the function using arguments from each
of the iterables.  Stops when the shortest iterable is exhausted.

Learn Python !

Two possibilities (among others I suppose...) :

sage: [F(u[0], u[1]) for u in L2]
[0, -3, -6, -9, -2, 1, 1, -2, -8, -1, 2, 5, -18, -7, 0, 3]
sage: list(map(lambda u:F(*u), L2))
[0, -3, -6, -9, -2, 1, 1, -2, -8, -1, 2, 5, -18, -7, 0, 3]`

Building `L2 isn't necessary :

sage: [F(*u) for u in Set(L0).cartesian_product(Set(L1))]
[0, -2, -8, -18, -3, 1, -1, -7, -6, 1, 2, 0, -9, -2, 5, 3]

I suppose that the itertools standard Pythonlibrary offers other possibilities...

Personally, I'd dispense with L2 and would simply do :

sage: table([[F(u, v) for v in L1] for u in L0], header_column=["F"]+L0, header_row=L1)
  F | 0    1    2    3
+---+----+----+----+-----+
  0 | 0    -2   -8   -18
  1 | -3   1    -1   -7
  2 | -6   1    2    0
  3 | -9   -2   5    3

Learn Python !

HTH,

Two possibilities (among others I suppose...) :

sage: [F(u[0], u[1]) for u in L2]
[0, -3, -6, -9, -2, 1, 1, -2, -8, -1, 2, 5, -18, -7, 0, 3]

You can pass a list (or other iterable) of arguments via indirection :

sage: [F(*u) for u in L2]
[0, -3, -6, -9, -2, 1, 1, -2, -8, -1, 2, 5, -18, -7, 0, 3]

or equivalently (see map?) :

sage: list(map(lambda u:F(*u), L2))
[0, -3, -6, -9, -2, 1, 1, -2, -8, -1, 2, 5, -18, -7, 0, 3]`

Building `L2 isn't necessary :

sage: [F(*u) for u in Set(L0).cartesian_product(Set(L1))]
[0, -2, -8, -18, -3, 1, -1, -7, -6, 1, 2, 0, -9, -2, 5, 3]

I suppose that the itertools standard Pythonlibrary offers other possibilities...

Personally, I'd dispense with L2 and would simply do :

sage: table([[F(u, v) for v in L1] for u in L0], header_column=["F"]+L0, header_row=L1)
  F | 0    1    2    3
+---+----+----+----+-----+
  0 | 0    -2   -8   -18
  1 | -3   1    -1   -7
  2 | -6   1    2    0
  3 | -9   -2   5    3

Learn Python !

HTH,