Yes, the accounts are premium tier, so they will have both desktop and mobile access.
https://www.lastpass.com/pricing
Hello @gllerner,
Welcome to the LastPass Community!
That is correct when you pay for a subscription you can use unlimited devices to access your LastPass account. You can simultaneously use your LastPass app on the phone and use the LastPass extension or website in the computer and you will not have any problem.
Kind Regards,
Alejandra
LastPass Support