Apply MapThread to all but one variable

Here's one way to do it with Outer:

n = 3;
l1 = Array[a, n];
l2 = Array[b, n];
l3 = Array[c, n];

Outer[
  f[#1[[1]], #1[[2]], #2] &,
  Transpose @ {l1, l2},
  l3,
  1
]

Out[25]= {{f[a[1], b[1], c[1]], f[a[1], b[1], c[2]], f[a[1], b[1], c[3]]}, {f[a[2], b[2], c[1]], f[a[2], b[2], c[2]], f[a[2], b[2], c[3]]}, {f[a[3], b[3], c[1]], f[a[3], b[3], c[2]], f[a[3], b[3], c[3]]}}

a = {a1, a2, a3, a4, a5};
b = {b1, b2, b3, b4, b5};
c = {c1, c2, c3, c4, c5};

Table[f[a[[j]], b[[j]], c[[k]]], {j, 1, 5}, {k, 1, 5}]

Another possibility is to use the 3-arg version of Thread. With Sjoerd's example:

n = 3;
l1 = Array[a,n];
l2 = Array[b,n];
l3 = Array[c,n];

Using Thread:

Thread /@ Thread[f[l1, l2, l3], List, 2]

{{f[a[1], b[1], c[1]], f[a[1], b[1], c[2]], f[a[1], b[1], c[3]]}, {f[a[2], b[2], c[1]], f[a[2], b[2], c[2]], f[a[2], b[2], c[3]]}, {f[a[3], b[3], c[1]], f[a[3], b[3], c[2]], f[a[3], b[3], c[3]]}}