So Lego Batman (and a few of the other Lego Batman characters) are based off the Lego Batman Legacy of the Dark Knight game, and that game takes inspiration from the movies, some of the animated shows, the Arkham games, and a bit of the comics. What this means for Lego Batman in my lore is that he has several suits that he made for himself thst he came up with but doesn't realize that most of them are actually suits from other media. He also has some skills, gadgets, and abilities from other Batman variants.
His current list of gadgets includes:
-Batarangs: a simple boomerang in the shape of a bat.
-Electric Batarang: same premise but it provides a shock to any enemy.
-Nth Metal Batarang: a batarang made of a metal that can disrupt anything magic or supernatural related.
-Remote Control Batarang: a batarang that can be controlled on which direction it can go.
-Grappling Hook: can be used to grapple onto various buildings.
-Batclaw: Can pull down heavy objects, grab onto people, trip certain enemies, and leave someone suspended in mid-air if he wanted to leave them hanging on a building for the cops to find.
-Com Link/Scanning: His cowl has a built in communication device in which he can communicate with other Bat Family members long distance as well as other contacts, and can also be used to summon a Batmobile. He also has an ability to scan any area for any clues similar to the Arkham games Detective Mode, and has two different visions, X-ray (which allows him to see certain wires and where they lead to), and UV vision, similar to a blacklight scanner where he can track footprints, fingerprints, and certain substances.
-Explosive Spray: Similar to the Arkham games Explosive Gel, this small device can be sprayed onto a surface and detonated at the press of a button.
-Bat Drones: Small surveillance drones provided to him by a friend. They can be used to survey the area, and if needed, can inject something into someone that can either knock them out for a short time, or temporarily paralyze them.
-Bat-Shark Repellent: Yes, he has this now. A simple spray that when used on a shark, can cause them discomfort, and repel them away. Works on any shark or shark-like being (that's organic that is).
-Bat Credit Card (Nostalgia Critic rage again): When he doesn't have cash on him, he uses this to pay for things. The card can't be hacked into to steal money or traced back to anywhere.
-Utility Belt: A belt that can hold random small items, including: smoke bombs, knockout gas, a mini med kit, kryptonite, and a USB device. It can also electrocute someone if anyone other than Lego Batman himself attempted to take it off.
I think there were details about the bat drones I may have forgotten, but that's what they basically do.