Would I need a three-notched tool to remove this?
Three-hooked spanner is not necessary, but it would improve the engagement and decrease chance of stripping a notch on the BB lockring. Parktool makes the HCW-5 spanner, which combines both a three-hook and a single hook. Here's a relevant quote:
One side is a single hook, the other is a hook spanner with 3 notches for better engagement in the lockrings.
There's two parts to this - the circular lockring around the outside and the cup.
I'm a bad and lazy mechanic and I use a pair of sliding lockjaw adjustable pliers to remove the lockring (assuming its not just hand-tight in the first place).
This tends to marr the outer edge of the lockring, but on an old beater bike that's not important.
You can use a rag to protect the finish from the jaws. The hooked tools never work very well in my personal experience, but YMMV
I've also used a hammer and drift on particularly stubborn ones, as well as gentle heat from a propane torch. Once I used an automatic center punch to shock-loose a lockring cos it was the only tool available at the time.
To remove the cup you can use a 12" adjustable spanner, but the flats are really small and the tool slips easily. The proper tool is something like a https://www.parktool.com/product/adjustable-cup-wrench-hcw-11
Sometimes you can undo the cup and the lockring just comes with it. Also note the left cup is generally normal-threadded (ie RTLL)