Kevin's answer is the most common usage, definitely. Be aware that it can have a different meaning: "got lucky" can be a euphemism for having sex. But context would usually make the first meaning clear.

It would be used as a self-deprecating comment, meaning that your actions did not have much influence on a successful outcome. For example, you are selected for a better job. If someone asks how did you get the job, instead of saying, "Because I worked hard", you might just say "I just got lucky." It is often used so people do not think you are boasting.

I think I'll get lucky tonight (future) is for sex. When it happens, a person does not then suggest it was luck. At that time, It is not going to be attributed to anything but the persons own assets. So, "I just got lucky" (recent past) is for when something good and unexpected happens, such as finding or winning something by chance.

Luck How did you get such a high paying job? I just got lucky. Sex I just got lucky last night! What was her name? If you begin a statement with it , it regards sex. If it is an answer to a question, it regards actual luck.

I just got lucky could refer to having sex or it could mean you have been lucky - i.e. you have just won the Lotto - you got lucky and won and lot of money.