The first link you give for "Cable" is not a cable, it is a controller with display/throttle unit. Based on the battery info below, it is twice as powerful as your battery can handle. See notes below the battery stuff for more on that.
A quick search for "7A scooter controller" actually pops up a Lime controller
36v, 7A, B-WZKB3615A-LB-F4. If the item up for sale is tested, we will state so clearly. We are not a giant corporate entity. We appreciate your cooperation.
www.ebay.com
and ebay shows this as related
Lime Scooter Digital Display LSDP4.0
www.ebay.com
but I don't know if it is compatible with the controller (or if either are the right one for your specific scooter).
Another link that search finds is this kit
with display and controller; it's a KT brand so there's a lot of info out there on how to set them up for various systems. It's connectors (and pretty much any other controller out there other than the original) are different than your scooter's, so you'll have to change them out for matching ones (like by cutting off the ones from your existing controller and reusing them) or change the ones on your scooter to match it's controllers, or just splice the wires together. (which ever way you do it, you're going to have to figure out which wires are which on your scooter by tracing them all out and drawing up a diagram for each wire in each cable). Any part the kit comes with you wont' need to use from your scooter, so for instance the "go button" will not be needed, instead you use the throttle from the kit. Etc.
The second link you give for battery site has the specs quoted below, which don't say how much current it can actually supply for either peak or continuous use. That means that there's no guarantee it will work on any specific controller or for any particular usage.
It does say it is "up to 250w" for motor power, which at 36v is 250 / 36 = 7A. The wording suggests a maximum, so whether it can do that for very long or not, I don't know. My guess is "probably", but you won't know until you test it and see what breaks at what current.
So whatever controller you get should have a current limit of maximum of 7A, preferably less. The one you linked as "Cable" is 13A on the label in one of the pictures and doesn't say what it is anywhere in the text of the page, so it's too powerful for the battery, and could damage it.
Those are just educated guesses, because neither one has complete specs, so we can't know what they'll really do.
Other notes:
The actual battery casing says max charging current of 10A, which is probably a terrible idea--it's almost certainly made of 18650 cells (the only cell info is "LG" which is a brand that makes all sorts of cells, and we don't know which ones it has so we don't know what they're capable of), and I am not aware of any of them that can charge that fast without getting unacceptably and unsafely hot, which could start a fire.
Under charging it says "loading time" is 2h, so a 3A charger is what you'd use for that, for a 6Ah pack.
As a 6Ah, it can't be 1p as there's no cells of the type it probably has in it with that capacity, so it has to be at least 10s2p or 20 cells. That's only important to guess what the pack is capable of; the 3A charging rate sounds reasonable, as does the 7A output, for a 2p 18650 pack for real LG cells of most (maybe any) model.
It doesn't say it has a BMS, so the cells are possibly completely unprotected, so it would be entirely up to you to monitor the individual cells during use, and charging to make sure none of them ever has a problem and overcharges or overdischarges (both of which can damage a cell, which can lead to a fire).
Battery Li-ion for Hoverboard Electric Scooter 36v 6000mAh Suitcase 20 Cells Black
Li-ion battery compatible with all kinds of 6,8,10 inch hoverboards
Capacity: 6Ah;
Voltage: 36V;
Cell technology: Li-Ion;
Cell Manufacturer: LG;
Size: 14 x 8 x 6 cm;
Weight: 1000g.;
Output: XT60-F;
Body type: ABS;
Motor power up to: up to 250 W
Specifications
GENERAL CHARACTERISTICS
| Product type | Battery |
| Compatibility | Hoverboard |
| Functions | Accumulator |
| Material | Plastic |
| Quantity/set | 1 |
| Content package | 1 x Battery |
| Color | Black |
TECHNICAL SPECIFICATIONS
| Battery type | Li-Ion |
| Battery capacity | 6 Ah |
| Loading time | 2 h |
| Power supply voltage | 36V |
DIMENSIONS
| Length | 140 mm |
| Width | 80 mm |
| Height | 60 mm |
| Weight | 1 Kg |
Manufacturer:
TERRA CELL
