Are these limits correct? $\lim_{n\to \infty}\text{sup} \frac{\lambda (n)}{n}=1$ and $\lim_{n\to \infty}\text{inf} \frac{\lambda (n)}{n}=0$ exist?

Question

I learned that from here for Euler totient function $\phi (n)$ , we have

$$\lim_{n\to \infty}\text{sup} \frac{\phi (n)}{n}=1$$

$$\lim_{n\to \infty}\text{inf} \frac{\phi (n)}{n}=0$$

However, I could not find such a limit for the Carmichael function $\lambda (n)$ which is associated with the Euler totient function. So I'm curious about the following limits:

$$\lim_{n\to \infty}\text{sup} \frac{\lambda (n)}{n}$$ and $$\lim_{n\to \infty}\text{inf} \frac{\lambda (n)}{n}$$

I think for any $n\in\mathbb{Z^{+}}$ we have $\phi(n)≥\lambda(n)$. So, are the following limits correct?

$\lim_{n\to \infty}\text{sup} \frac{\lambda (n)}{n}=1$ and $\lim_{n\to \infty}\text{inf} \frac{\lambda (n)}{n}=0$

I could not find these limits.

Thank you.