Firstly, you need an offer code to enable Dynamics AX for your organization account. For this, if you are an existing customer you can find details on how to get to the preview offer code from here and partners can find the details here.
Secondly, you need to be an administrator or you need to work with an administrator from your organization for the existing O365 account.
Steps the administrator needs to follow:
1. Open an in-private browser window
2. Navigate to the offer code that you get from the below location.
3. Click on "Sign in" on the top right corner
4. Sign-in with the administrator account for your tenant
5. Complete the sign-up process as shown below
6. Login to LCS, create a project and voilà you will have access to the new Dynamics AX through LCS.