@Bill D'Angelo
Azure Lab Services has inbound port restrictions and is really only made to be accessible through SSH or RDP. Trying to access the SQL services on the Lab Services VMs from on premises is not something that is currently supported. If you were able to run the desktop services also in the same or separate lab this should be supported.
For alternatives, you could have a single SQL Server and IIS VM that is outside of Lab Services, then provide connection instructions for the students. You could easily keep this VM available and just stop/start it as needed or you could create an image and then template of the server so you can easily recreate it. If you went the template route you could have each student launch from the template and they would have their own server to work with.
Azure for Students is a program offered by Microsoft Azure to provide students at Higher Education Institutions with access to various Azure cloud services and resources. Joining Azure for Students will grant you $100 in Azure credits with no credit card required. This credit will be valid for one year and you can renew each year you're an active student to get an addition $100. You also receive access to a set of free services you can deploy once you join. Select versions of Azure Virtual Machines, Azure SQL Databases, Azure Blob Storage and more are all free with your subscription. Hope this better answers your questions. Let me know if you still need assistance or have further questions.
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