test(lua): add integration test with multi-file fixture

3-file Lua fixture (user.lua, service.lua, main.lua) exercising:
- File detection across nested directories
- Function and method extraction (local, global, dot, colon syntax)
- require() import edge creation
- Cross-file call resolution

gitnexus/test/fixtures/lang-resolution/lua-app/lib/service.lua

@@ -0,0 +1,22 @@
+local User = require("lib.user")
+
+local Service = {}
+Service.__index = Service
+
+function Service.new()
+	local self = setmetatable({}, Service)
+	return self
+end
+
+function Service:create_user(name, email)
+	local user = User.new(name, email)
+	return user
+end
+
+function Service:process(user)
+	local greeting = user:greet()
+	print(greeting)
+	return greeting
+end
+
+return Service

gitnexus/test/fixtures/lang-resolution/lua-app/lib/user.lua

@@ -0,0 +1,19 @@
+local User = {}
+User.__index = User
+
+function User.new(name, email)
+	local self = setmetatable({}, User)
+	self.name = name
+	self.email = email
+	return self
+end
+
+function User:greet()
+	return "Hello, " .. self.name
+end
+
+function User:get_email()
+	return self.email
+end
+
+return User

gitnexus/test/fixtures/lang-resolution/lua-app/main.lua

@@ -0,0 +1,9 @@
+local Service = require("lib.service")
+
+local function main()
+	local svc = Service.new()
+	local user = svc:create_user("Alice", "alice@example.com")
+	svc:process(user)
+end
+
+main()

gitnexus/test/integration/resolvers/lua.test.ts

@@ -0,0 +1,59 @@
+/**
+ * Lua: basic pipeline integration — functions, methods, imports, calls.
+ * Verifies that the Lua language provider correctly parses module-pattern
+ * classes, colon-syntax methods, require() imports, and cross-file calls.
+ */
+import { describe, it, expect, beforeAll } from 'vitest';
+import path from 'path';
+import {
+  FIXTURES,
+  getRelationships,
+  getNodesByLabel,
+  edgeSet,
+  runPipelineFromRepo,
+  type PipelineResult,
+} from './helpers.js';
+import { isLanguageAvailable } from '../../../src/core/tree-sitter/parser-loader.js';
+import { SupportedLanguages } from '../../../src/config/supported-languages.js';
+
+const luaAvailable = isLanguageAvailable(SupportedLanguages.Lua);
+
+describe.skipIf(!luaAvailable)('Lua pipeline integration', () => {
+  let result: PipelineResult;
+
+  beforeAll(async () => {
+    result = await runPipelineFromRepo(path.join(FIXTURES, 'lua-app'), () => {});
+  }, 60000);
+
+  it('detects Lua files', () => {
+    const files = getNodesByLabel(result, 'File');
+    expect(files).toContain('main.lua');
+    expect(files).toContain('user.lua');
+    expect(files).toContain('service.lua');
+  });
+
+  it('extracts functions and methods', () => {
+    const functions = getNodesByLabel(result, 'Function');
+    const methods = getNodesByLabel(result, 'Method');
+    const allSymbols = [...functions, ...methods];
+    expect(allSymbols).toContain('main');
+    expect(allSymbols).toContain('new');
+    expect(allSymbols).toContain('greet');
+    expect(allSymbols).toContain('get_email');
+    expect(allSymbols).toContain('create_user');
+    expect(allSymbols).toContain('process');
+  });
+
+  it('extracts require() import edges', () => {
+    const imports = getRelationships(result, 'IMPORTS');
+    const importEdges = edgeSet(imports);
+    expect(importEdges.length).toBeGreaterThanOrEqual(1);
+  });
+
+  it('extracts call edges', () => {
+    const calls = getRelationships(result, 'CALLS');
+    expect(calls.length).toBeGreaterThanOrEqual(1);
+    const callNames = calls.map((c) => c.target);
+    expect(callNames).toContain('main');
+  });
+});