If I download LastPass portable to my Chrome installation on a USB stick, how do I stop that version syncing with my desktop Chrome?
You need to be logged in for it to sync. If the browser isn't even opened and you aren't logged in, then it won't be synced.
I think logging out is the best way to not let is sync.
then it can't sync.
I believe each instance of LastPass requires a separate log in, meaning until you logged in, your passwords wouldn't sync. At least, it wouldn't until you entered your LP key.
If you simply don't want to save your passwords, or want to change the way your account interacts with mobile accounts, there's a variety of options in the Last Pass account settings. Simply go to "preferences" and then "account settings".
You can read the user guide here.
Are you trying to stop the passwords within Lastpass from syncing or the Chrome extensions from syncing?
Why would you not want it to sync with your desktop? You'd want your data to be updated in all places no matter what right?
If you really don't want it to sync, just use a different email address for LastPass for your Chrome Portable instance versus your desktop instance -- then they're completely separated.