Rust specifically does not forbid deadlocks, including deadlocks caused by resource leaks. There are many ways in safe Rust to deliberately leak memory - either by creating reference count cycles, or the explicit .leak() methods on various memory-allocating structures in std. It's also not entirely useless to do this - if you want an &'static from heap memory, Box.leak() does exactly that.
Now, that being said, actually writing code to hold a LockGuard forever is difficult, but that's mainly because the Rust type system is incomplete in ways that primarily inconvenience programmers but don't compromise the safety or meaning of programs. The borrow checker runs separately from type checking, so there's no way to represent a type that both owns and holds a lock at the same time. Only stacks and async types, both generated by compiler magic, can own a LockGuard. You would have to spawn a thread and have it hold the lock and loop indefinitely[0].
[0] Panicking in the thread does not deadlock the lock. Rust's std locks are designed to mark themselves as poisoned if a LockGuard is unwound by a panic, and any attempt to lock them will yield an error instead of deadlocking. You can, of course, clear the poison condition in safe Rust if you are willing to recover from potentially inconsistent data half-written by a panicked thread. Most people just unwrap the lock error, though.