You will need to sign up for a monthly plan directly with LINE, so the number of messages that can be sent varies depending on the plan you select.
The "Free Plan" which is completely free of charge, you can send up to the quota given and this quota depends on the country you have signed up to in your LINE Official Account. When you reached your monthly limit, then Conversation API will sent status "FAILED" in delivery receipt and will state that this is a "CHANNEL_FAILURE", the description from LINE is "You have reached your monthly limit."
In the other paid plans, you can send up to the quota of included messages and after the quota has been used, then the additional message fees will apply. The maximum number of "additional messages" can be set within the limits set by yourself via the LINE Official Account Manager -> Settings -> Dashboard -> Set target limits. When the monthly limit and target is reached, then you can no longer send messages to any LINE users.
There are two ways to check the usage:
one option is by login to LINE Official Account Manager Dashboard
the other option is to keep count of the messages delivered as "push messages".
The Sinch Developer Documentation site contains comprehensive documentation and tutorials, which show you how we support LINE through the Sinch Conversation API.