So in solid metals they atoms give off electrons, which are delocalised and hold together all the metal atoms. But that's not the case in liquid metals, right? What holds together the individual atoms of liquid metals? Does it work similar to liquid nobel gasses, so spontaneous dipol moments? Or is there something else, like a few delocalised electrons, but not enough to form a solid?
"But that's not the case in liquid metals, right?" - That is the case. In liquid metals the fluid is still hold together by the same principle, it just happens that the heat energy in the material (vibration of the atoms) overcomes the energy that holds the atoms in place, but the metal is still pretty much sharing electrons.
So in solid metals they atoms give off electrons, which are delocalised and hold together all the metal atoms.
More like the other way around: the crystal lattice of metal ions en masse will hold the valence electrons together as a dynamic charge cloud which surrounds and permeates the lattice.
Above the metal's melting point the long-range ordered structure of the ion lattice breaks down due to the higher kinetic energies. Short range ordering may persist for a temperature range above the melting point. But the valence electrons are nonetheless enveloped around the liquid metal ions, albeit with weaker forces as well as a tendency for the liquid metal ions themselves to evaporate under low pressures.