St. Louis is likely to attempt to sign the 26-year-old Heyward to a multiyear deal. He hit .293 with 13 homers and 60 RBIs, and he is an NL Gold Glove finalist.
The 37-year-old Lackey became the ace after Adam Wainwright was sidelined with a torn left Achilles. Lackey went 13-10 with a career-best 2.77 ERA. He started in Games 1 and 4 of the NL Division Series against the Chicago Cubs.
Players have until Nov. 13 to accept the offers. If either or both sign elsewhere, St. Louis would receive an extra pick per player after the first round of June's amateur draft.