You can use the same alias, but you'll need to generate a new pubkey for the CLN node.
Discussion
nostr:npub19tcpurtt6xulhw0r6sc404j9jraj0h8me2lzs7z2tqewz7l0hpas59nlea
What happens on your website when an alias is being recycled with a completely new node? Assuming the previous one never comes back on the network, of course…
Could this bring confusion in search results?
It can be a bit confusing at times, but it's usually obvious when looking at the capacity and number of channel of the node in the search results.
"Satbase" for example has been used as an alias in the past on a now-defunct node and it is also in use by an active node.