Delta recently moved to terminal 2 and terminal 3 at LAX. If your outbound flight is a codeshare on another airline (with a DL flight number), then it might also depart from the "International" terminal, also known as the "Tom Bradley International Terminal", TBIT, or Terminal B.
As both flights are on Delta (or a codeshare partner) you will not need to re-check bags - they will be transfers to your new flight for you.
Depending on which terminal you land in and depart from you may need to move between terminals. Terminal 2, 3 and B are NOT connected airside, however there is a air-side shuttle that can be used to move between these terminals without the need to clear security. You should be careful not to accidentally leave the secured area, or you will need to re-clear security which could take some time (although likely not at that time of night)
90 minutes should be plenty of time to make this connection, even if you need to catch the bus between terminals. Of course, that presumes that your inbound flight is not delayed - a delay of anything more than about an hour could turn this into a very tight connection, but of course that's always possible regardless of how much time you leave!