Hmm. "lobster bag". Gotta search that term now.
Sorry if I seem naïve on some of these terms. I'm a freshwater guy, so I miss some things that might seem obvious in retrospect...
The thing I'm imagining would look more like a small rope bag, somewhere between
this (a "line mug" for holding throwing line for arboreal climbing) and
this, (a rope bag for canyoneering).
I think having some structural integrity to it, (holding itself open in a cylindrical shape), would give lures less opportunity to hook both sides and turn the whole thing into a solid structure that must be cut apart. I'm thinking the line mug is actually pretty close to what I want, (5" diameter, 6"-8" tall), but I'd make the tube extend past the top and bottom an inch, put some manner of reinforced drain holes in the base and ... I don't know for the top.