For Linux distributions, you need to perform an additional step i.e. opening the RDP from the IP4 Firewall. Steps:

1. Go to your LightSail instance
2. Networking Tab
3. IPv4 Firewall > Add Rule
4. Under Application Choose "RDP"
5. Click on Create

After a lot of struggle I found this option. For Windows instances RDP works by default, but for Linux distributions this needs to be done additionally.