diff --git a/compiler/src/dotty/tools/dotc/transform/LambdaLift.scala b/compiler/src/dotty/tools/dotc/transform/LambdaLift.scala
index 81a114e03fbc..17772df9b91c 100644
--- a/compiler/src/dotty/tools/dotc/transform/LambdaLift.scala
+++ b/compiler/src/dotty/tools/dotc/transform/LambdaLift.scala
@@ -100,7 +100,7 @@ class LambdaLift extends MiniPhase with IdentityDenotTransformer { thisTransform
      *  Note: During tree transform (which runs at phase LambdaLift + 1), liftedOwner
      *  is also used to decide whether a method had a term owner before.
      */
-    private val liftedOwner = new HashMap[Symbol, Symbol]
+    private val liftedOwner = new LinkedHashMap[Symbol, Symbol]
 
     /** The outer parameter of a constructor */
     private val outerParam = new HashMap[Symbol, Symbol]
diff --git a/tests/run/i2738.check b/tests/run/i2738.check
new file mode 100644
index 000000000000..1261ac914586
--- /dev/null
+++ b/tests/run/i2738.check
@@ -0,0 +1,8 @@
+foo
+bar$1
+foo
+bar$2
+baz
+Test$qux$2$
+baz
+Test$qux$4$
diff --git a/tests/run/i2738.scala b/tests/run/i2738.scala
new file mode 100644
index 000000000000..b7c87e0dc8f9
--- /dev/null
+++ b/tests/run/i2738.scala
@@ -0,0 +1,49 @@
+object Test {
+
+  def main(args: Array[String]): Unit = {
+    foo(1)
+    foo("a")
+    baz(2)
+    baz("b")
+  }
+
+  def foo[X <: Int](x: X) = {
+    def bar = printlnThisMethodName()
+    printlnThisMethodName()
+    bar
+  }
+
+  def foo(x: String) = {
+    def bar = printlnThisMethodName()
+    printlnThisMethodName()
+    bar
+  }
+
+  def baz[X <: Int](x: X) = {
+    object qux {
+      override def toString() = {
+        printlnThisMethodsClassName()
+        "a"
+      }
+    }
+    printlnThisMethodName()
+    qux.toString()
+  }
+
+  def baz(x: String) = {
+    object qux {
+      override def toString() = {
+        printlnThisMethodsClassName()
+        "b"
+      }
+    }
+    printlnThisMethodName()
+    qux.toString()
+  }
+
+  def printlnThisMethodName() =
+    println(Thread.currentThread().getStackTrace()(2).getMethodName)
+
+  def printlnThisMethodsClassName() =
+    println(Thread.currentThread().getStackTrace()(2).getClassName)
+}