Some networks allow you to check your messages online but without knowing which network you are on, it is impossible for me to give you specific instructions unfortunately.
That doesn't mean you should give up - there are several things you can do to try and access your device's messages.
How to check messages on a phone you've lostIf you search for your network on Google, you will find their website, and on there it should tell you what you need to know.
You might find there is a members area that you can join and from there you can access all sorts of details about your account, such as when your next bill is due and how much it will be.
The alternative is to call your network, tell them your phone has been lost and request a replacement Sim card. You may find that any messages you have received since losing your phone will be stored safely on the new Sim.
If not, maybe your network can tell you if there is a way to get them back, it's worth asking!