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Here's some ways. Using:

l = {1+2*s,2+3*s,4+1*s};
slist = {1, 2, 3};

The answer closest to what you asked is

{1 + 2*s, 2 + 3*s, 4 + 1*s} /. s -> slist // Diagonal

However, that does 3^2 - 3 too many calculations, so here's some more ways:

MapThread[#1 /. s -> #2 &, {l, slist}]
MapThread[ReplaceAll, {l, Thread[s -> slist]}]
ReplaceAll @@@ Transpose[{l, Thread[s -> slist]}]
MapIndexed[First@#1 /. s -> Last@#1 &, Transpose@{l, slist}]
MapIndexed[#1 /. s -> slist[[First@#2]] &, l]

If s is always going to be the list {1, 2, 3, ...}, then:

MapIndexed[#1 /. s -> First@#2 &, l]