No, the numbers selected when the subscription is started will be used for every subsequent drawing.
While there is no way to randomize the numbers after you set the subscription, you can use the Quick Pick tool when creating the subscription order. These numbers will be used for subsequent drawings in accordance with the original order.
To choose new numbers, you can set up a new subscription.
You can have multiple subscriptions on your Lotto.com account, so you do not have to cancel your active subscriptions to make room for more.