The Soyuz spacecraft was originally developed for a moonshot attempt. This goal was abandoned when the US beat them to the moon, but the capsule was still developed with lunar capability in mind.
It's important to understand, however, that Soyuz isn't a single capsule design - it's a family of over 9 distinct spacecraft types:
— Soyuz A
— Soyuz 7K-OK
— Soyuz 7K-L3
— Soyuz 7K-T
— Soyuz 7K-TM
— Soyuz T
— Soyuz TM
— Soyuz TMA
— Soyuz TMA-M
The proposed Soyuz-K is one of the family, but one which has not been flown yet.
The name Soyuz is also used for a series of rockets used to launch Soyuz spacecraft.
The current capsules are intended for under 4 days of operation; that said, it's mostly a matter of additional life support (food, water, oxygen, and CO2 scrubber) for a lunar shot. 3.5 kL is pretty tight for a 3 person craft, but it's not unreasonable.
The Soyuz TMA-01 mission operated from roughly 23:11 Thursday to 00:01 sunday in autonomous mode - just shy of 49 hours of operational flight - prior to docking, and another 2:36 of operation for landing. The TMA-02M and TMA-03M missions are of similar flight time. Apollo 13, on it's lunar flyby, had a total elapsed mission time of 5 days, showing that the capsule would need to be carrying some extra supplies.
This is why the plans were not for a TMA-M, per se, but the "Soyuz-K" configuration. This is a TMA-M with a modified Orbital Habitation Module, and one or more orbital tug modules added. An off-the-shelf orbital tug, the Fregat, has enough delta-V to put a TMA-M with an endurance oriented habitation module into circumlunar flight, similar to the overall flown Apollo 13 mission of around 6 days. The Fregat module would be launched separately on a Proton rocket flight, and docked in orbit.
Other variations could include additional habitat, larger thrust units, or even a lander, launched aboard one or more additional flights, and docked in orbit.