error[E0373]: closure may outlive the current function, but it borrows `self`, which is owned by the current function
  --> $DIR/issue-62097.rs:13:13
   |
LL |         foo(|| self.bar()).await;
   |             ^^ ---- `self` is borrowed here
   |             |
   |             may outlive borrowed value `self`
   |
note: function requires argument type to outlive `'static`
  --> $DIR/issue-62097.rs:13:9
   |
LL |         foo(|| self.bar()).await;
   |         ^^^^^^^^^^^^^^^^^^
help: to force the closure to take ownership of `self` (and any other referenced variables), use the `move` keyword
   |
LL |         foo(move || self.bar()).await;
   |             ++++

error[E0521]: borrowed data escapes outside of method
  --> $DIR/issue-62097.rs:13:9
   |
LL |     pub async fn run_dummy_fn(&self) {
   |                               -----
   |                               |
   |                               `self` is a reference that is only valid in the method body
   |                               let's call the lifetime of this reference `'1`
LL |         foo(|| self.bar()).await;
   |         ^^^^^^^^^^^^^^^^^^
   |         |
   |         `self` escapes the method body here
   |         argument requires that `'1` must outlive `'static`

error: aborting due to 2 previous errors

Some errors have detailed explanations: E0373, E0521.
For more information about an error, try `rustc --explain E0373`.