So, basically, Lightsail is pretty much a prebuilt EC-2 instance, which is what they call essentially a computer on their systems, designed for simplicity to get up and running quickly, but as a result, you do loose some flexibility with it.
EC-2 is essentially a full computer that you can remote into from anywhere and do anything that you can do on a computer.
Some advantages to Lightsail over EC-2:
Set monthly pricing based on what you need
Easy to setup and maintain
Simple to understand
Some advantages to EC-2 over Lightsail:
Fully scaleable in real time, when you need more power, EC-2 instance can be added automatically in the background and when less is needed, it can be automatically closed. Lightsail can scale to a point, but not to the same degree and not as much in real time.
Pay for only what you use
Has tiers that are free for an entire year and that may very well include data transfers.
Inbound data transfers don't usually count again your data limits, not sure about on Lightsail.
Has more options for types of computers and operating systems
Can run an image of your existing system if you so choose
Basically, if you setup your own web server locally, you should be able to setup and configure an EC-2 instance without much difficulty, as it is essentially the same thing, you are just doing it remotely instead of physically where you are and you have to create the instance first.
Now which one is right for your needs? Well, in the end only you can decide that, they both have pluses and minuses.