About the cable lock mechanism

Sennheiser uses a "twist to lock" mechanism on their HD 5XX series of headphones. (This series includes the HD 559, HD 599, HD 560S, and other headphones with the same chassis.) This is a non-standard mechanism which requires compatible audio cables. These cables can be twisted when inserted to lock them into place, and twisted again to be unlocked for removal. In addition, these headphones have a 2.5 mm jack instead of the more common 3.5 mm jack. The jack is inside the left earcup.

Take a look at the 2.5 mm end (the end that plugs into your headphones) of your compatible cable. It has grooves cut into the end of its sheath which allows it to fit into the headphones and lock/unlock when twisted. The fact that the grooves are immediately below the plug means that there must be a complementary component inside the headphones, between the cable entry hole and the jack, whose protrustions precisely fit into the grooves. Luckily the cable lock component isn't built into the cup, which means it's removable.

Reasons to remove the lock

Spend less money on cables. The cable lock limits your cable options to the official Sennheiser cables and a few aftermarket cables. None of these cables are great and they're all relatively expensive. You can get custom cables made, but that's even more expensive.
Spend less money on adapters. Because the cable lock requires compatible cables, you would need an adapter to use any other cables. I'm only aware of one — which converts the Sennheiser locking connector to a standard 3.5 mm jack — and it's much more expensive than regular 2.5 mm plug to 3.5 mm jack adapters. Plus, it limits you to unbalanced audio.
Use any cable you want. With the lock removed, you would be able to use any cable or adapter with a 2.5 mm plug. This opens your options to cables of a variety of lengths and materials, cables with integrated controls or boom mics, balanced cables, and more.
Cables won't drag your headphones with them. Because the lock keeps your cable firmly attached to your headphones, if your cable gets caught on something, the cable won't simply disconnect from the headphones. Instead, your headphones might be pulled off your head and even crash into the ground. You could prevent this by not locking your cable, but mine would sometimes lock unintentionally.
You can still use your compatible locking cables. Because the protrusions are on the lock component and not the compatible cables, these cables will still fit into the headphones if the lock is removed.

Reasons to leave the lock alone

Remain under warranty. Sennheiser provides a two year warranty on newly purchased headphones. By removing the cable lock on my pair, I voided my warranty. I wasn't concerned because this series of headphones is known for having great build quality and lasting a decade or more.
Maintain a consistent audio connection. The cable lock component also decreases the size of the cable entry hole. If you decide to remove the cable lock component entirely instead of disabling the lock and putting it back, your cable might not fit as snugly into the jack. This could cause you to occasionally lose audio in the right earcup until you push the jack back in.
You're happy with the existing cable and adapter options. There's not much reason to attempt to remove the lock if you don't have issues with the official and unofficial compatible cables, don't have a need for different types of cables, or are willing to pay for compatible adapters.
You're willing to build or buy a custom cable. If you have a soldering iron and are willing to spend the time, making your own cable isn't too hard. It might also make sense to pay for one, especially if you already have an interconnect system.

How to remove the lock

Open the left earcup

First, remove the left earpad. It has a ring on its underside which snaps in place beneath eight equally-spaced ridges on the earcup. More specifically, these ridges are on the outer edge of the cover that protects the driver. Simply pull the earpad away from the earcup, one part at a time, to release it from the ridges.

Next, remove the cover. It's held in place by three small screws around its perimeter. Be very careful while removing the cover! The driver is attached to the cover and there are wires connecting the driver to the earcup. I moved my headphones onto a cotton sheet for this step so that I could gently support the cover with a bundle of fabric.

Take out the lock component

The cable lock component is a shaped like a small plastic cylinder with two "wings" that are each held down by a single screw. At least on my headphones, the cylinder had < PCM > and T1-4 written on it in raised text. The component is placed between the cable entry hole and the jack. The jack is hidden under a circuit board that transmits the left and right audio signals to the driver.

Aside: You might notice that there are four signal wires soldered to the circuit board: left channel audio (L+), inverted left channel audio (L-), right channel audio (R+), and inverted right channel audio (R-). This confirms the "rumour" that the headphones are capable of producing balanced output. It also explains why the Sennheiser locking connector uses a 2.5 mm TRRS plug.

On the HD 560S, which is the latest model in the series and the model that I own, the lock is glued in place. I used a flat screwdriver to pry it off, but I had to be careful because it was stuck very tightly. I started by lifting at the "wings" because they extend further than their threaded inserts. This released the bottom end of the component, so I started lifting from there until the top end also released.

Disable the lock

This step is optional but recommended. Now that you've removed the cable lock component from the earcup, you will be able to insert any 2.5 mm plug into the jack that you want. However, the component does more than just lock cables. It also has a "ledge" at the bottom which reduces the size of the cable entry hole, helping to guide the plug and ensure that it fits snugly into the jack. I'm not sure, but it might also help support the jack and/or circuit board.

To disable the lock, you will have to remove the protrusions inside the cylinder. You can do this with a knife, metal file, or any other object that can smooth out the bumps. If you don't want to modify the original component, you can make a copy of it with a 3D printer. You can even try removing the protrusions from the scanned mesh before printing the copy. Afterwards, push the lock-less component back into place and screw it down.

Close the left earcup

Hooray, you've completed the mod! Test that the drivers work by plugging your audio cable into your headphones and your source. Try not to move the headphones if the cover is still open. Ensure that you can hear audio from both earcups. You can listen through the outsides of the earcups if your headphones are open-back.

If there are no issues, screw the cover back into place and reinstall the earpad. You have to press it into the cover until the ring has snapped into place under all the ridges. Finally, enjoy your modded headphones! If you still have the original cable lock mechanism, or a copy, you can reverse the mod whenever you'd like.