Would antimatter in a solid form, anti-lithium for example, be easier to store than gaseous anti-hydrogen or just plain positrons?
We don't know how to make solid chunks of antimatter. However, if we could do it, then it should be much easier to store a solid chunk than a gas.
I can imagine several different ways to keep the chunk suspended in a vacuum: via diamagnetic repulsion, electromagnetic suspension, electrostatic repulsion, or photon pressure.
The temperature would need to be kept close to absolute zero, because most solids have a finite vapor pressure and any atoms that floated away from the chunk would annihilate as soon as they reach the normal-matter container.
The problem with antimatter, regardless of its phase, is that it annihilates into light as soon as it comes into contact with matter.
So you always have to make sure that your contained in empty (there is a good vacuum inside), and that the antimatter does not touch the walls.
I don't actually know how antimatter is usually stored, if anyone has ever done it. But ions and neutral atoms can be trapped (Pauli, TOP, optical dipole traps for example), and the principles behind these should also be valid for antimatter.