No, virtually there is no limit on the number of invites you can send in a day, week or month from Let's Calendar's end.
To send calendar invites as per your requirements you need to keep in mind two things -
Credits in Let's Calendar
Let's Calendar provides you with "Credits" as per your plan, and upon expiry of your credits, you will be charge an overrage charge as per your plan on the extra number of invites/credits being utilized.
Sending limits enforced by your Email Service Provider
As you have integrated, and are using your own Email Service Provider (Sendgrid, Mailgun, O365 or Google) to send out the calendar invites, there will be some limitations and restrictions enforced by them. Please check these limitations and ensure you are not restricted by them.