diff --git a/lib/lua/test.sh b/lib/lua/test.sh
index 96a2e495..f644888a 100755
--- a/lib/lua/test.sh
+++ b/lib/lua/test.sh
@@ -409,6 +409,57 @@ cat > "$TMPFILE" << 'EPOCHS'
 (epoch 484)
 (eval "(lua-eval-ast \"local s = 0 for i = 1, 100 do s = s + i end return s\")")
 
+;; ── Phase 3: functions + closures ─────────────────────────────
+;; Anonymous
+(epoch 500)
+(eval "(lua-eval-ast \"local f = function(x) return x + 1 end return f(5)\")")
+(epoch 501)
+(eval "(lua-eval-ast \"local f = function() return 42 end return f()\")")
+(epoch 502)
+(eval "(lua-eval-ast \"return (function(a, b) return a * b end)(3, 4)\")")
+
+;; Local function
+(epoch 510)
+(eval "(lua-eval-ast \"local function double(x) return x * 2 end return double(7)\")")
+(epoch 511)
+(eval "(lua-eval-ast \"local function sum3(a, b, c) return a + b + c end return sum3(1, 2, 3)\")")
+(epoch 512)
+(eval "(lua-eval-ast \"local function greet() return \\\"hi\\\" end return greet()\")")
+
+;; Top-level function decl
+(epoch 520)
+(eval "(lua-eval-ast \"function add(a, b) return a + b end return add(3, 4)\")")
+(epoch 521)
+(eval "(lua-eval-ast \"function id(x) return x end return id(\\\"abc\\\")\")")
+
+;; Closures — lexical capture
+(epoch 530)
+(eval "(lua-eval-ast \"local x = 10 local function getx() return x end return getx()\")")
+(epoch 531)
+(eval "(lua-eval-ast \"local function make_adder(n) return function(x) return x + n end end local add5 = make_adder(5) return add5(10)\")")
+(epoch 532)
+(eval "(lua-eval-ast \"local function counter() local n = 0 return function() n = n + 1 return n end end local c = counter() c() c() return c()\")")
+(epoch 533)
+(eval "(lua-eval-ast \"local a = 1 local b = 2 local function f() return a + b end a = 10 return f()\")")
+
+;; Recursion
+(epoch 540)
+(eval "(lua-eval-ast \"local function fact(n) if n <= 1 then return 1 else return n * fact(n - 1) end end return fact(5)\")")
+(epoch 541)
+(eval "(lua-eval-ast \"function fib(n) if n < 2 then return n else return fib(n-1) + fib(n-2) end end return fib(10)\")")
+
+;; Higher-order
+(epoch 550)
+(eval "(lua-eval-ast \"local function apply(f, x) return f(x) end local function sq(n) return n * n end return apply(sq, 4)\")")
+(epoch 551)
+(eval "(lua-eval-ast \"local function twice(f, x) return f(f(x)) end return twice(function(n) return n + 1 end, 5)\")")
+
+;; Mixed with control flow
+(epoch 560)
+(eval "(lua-eval-ast \"local function max(a, b) if a > b then return a else return b end end return max(7, 3)\")")
+(epoch 561)
+(eval "(lua-eval-ast \"local function sum_to(n) local s = 0 for i = 1, n do s = s + i end return s end return sum_to(10)\")")
+
 EPOCHS
 
 OUTPUT=$(timeout 60 "$SX_SERVER" < "$TMPFILE" 2>/dev/null)
@@ -633,6 +684,32 @@ check 482 "while i<5 count"                 '5'
 check 483 "repeat until i>=3"               '3'
 check 484 "for 1..100 sum"                  '5050'
 
+# ── Phase 3: functions + closures ─────────────────────────────
+check 500 "anon fn call"                    '6'
+check 501 "anon fn no args"                 '42'
+check 502 "iife"                            '12'
+
+check 510 "local function double"           '14'
+check 511 "local function sum3"             '6'
+check 512 "local function greet"            '"hi"'
+
+check 520 "top-level function decl"         '7'
+check 521 "top-level id string"             '"abc"'
+
+check 530 "closure reads outer"             '10'
+check 531 "closure factory add5(10)"        '15'
+check 532 "closure with mutable counter"    '3'
+check 533 "closure sees later mutation"     '12'
+
+check 540 "recursive local fact(5)"         '120'
+check 541 "recursive top-level fib(10)"     '55'
+
+check 550 "apply(sq,4)"                     '16'
+check 551 "twice(+1, 5)"                    '7'
+
+check 560 "max with if"                     '7'
+check 561 "sum_to(10) with for"             '55'
+
 TOTAL=$((PASS + FAIL))
 if [ $FAIL -eq 0 ]; then
   echo "ok $PASS/$TOTAL Lua-on-SX tests passed"
diff --git a/plans/lua-on-sx.md b/plans/lua-on-sx.md
index 9ae8fe61..8f1d8c17 100644
--- a/plans/lua-on-sx.md
+++ b/plans/lua-on-sx.md
@@ -51,7 +51,7 @@ Each item: implement → tests → tick box → update progress log.
 - [x] 30+ eval tests in `lib/lua/tests/eval.sx`
 
 ### Phase 3 — tables + functions + first PUC-Rio slice
-- [ ] `function` (anon, local, top-level), closures
+- [x] `function` (anon, local, top-level), closures
 - [ ] Multi-return: return as list, unpack at call sites
 - [ ] Table constructors (array + hash + computed keys)
 - [ ] Raw table access `t.k` / `t[k]` (no metatables yet)
@@ -82,6 +82,7 @@ Each item: implement → tests → tick box → update progress log.
 
 _Newest first. Agent appends on every commit._
 
+- 2026-04-24: lua: phase 3 — functions (anon/local/top-level) + closures verified (lexical capture, mutation-through-closure, recursion, HOFs). 175 total tests.
 - 2026-04-24: lua: phase 2 transpile — arithmetic, comparison, short-circuit logical, `..` concat, if/while/repeat/for-num/local/assign. 157 total tests green.
 - 2026-04-24: lua: parser (exprs with precedence, all phase-1 statements, funcbody, table ctors, method/chained calls) — 112 total tokenizer+parser tests
 - 2026-04-24: lua: tokenizer (numbers/strings/long-brackets/keywords/ops/comments) + 56 tests