How about this

build.hxml

@@ -4,5 +4,4 @@
 -dce full
 -lib hxnodejs
 -D analyzer-optimize
-
 --cmd yarn build

build/index.js

@@ -365,12 +365,19 @@ exports.getState = getState;
 (function ($global) { "use strict";
 var Main = function() { };
 Main.main = function() {
-	var args = ["global","add","lix@" + __webpack_require__(470).getInput("lix-version")];
+	var core = __webpack_require__(470);
+	var args = ["global","add","lix@" + core.getInput("lix-version")];
 	if(args == null) {
 		js_node_ChildProcess.spawnSync("yarn",{ shell : true, stdio : "inherit"});
 	} else {
 		js_node_ChildProcess.spawnSync("yarn",args,{ stdio : "inherit"});
 	}
+	var path = StringTools.replace(js_node_ChildProcess.execSync("yarn global bin").toString(),"\n","");
+	core.addPath(path);
+};
+var StringTools = function() { };
+StringTools.replace = function(s,sub,by) {
+	return s.split(sub).join(by);
 };
 var js_node_ChildProcess = __webpack_require__(129);
 Main.main();

src/Main.hx

@@ -1,7 +1,13 @@
+import js.node.ChildProcess;
+import js.node.Buffer;
+using StringTools;
+
 class Main {
 	static function main() {
-		var version = js.Lib.require('@actions/core').getInput('lix-version');
+		var core = js.Lib.require('@actions/core');
-		// js.Lib.require('@actions/exec').exec('yarn global add lix@$version');
+		var version = core.getInput('lix-version');
 		Sys.command('yarn', ['global', 'add', 'lix@$version']);
+		var path = (ChildProcess.execSync('yarn global bin'):Buffer).toString().replace('\n', '');
+		core.addPath(path);
 	}
 }