The problem with lava is that it isn't a single compound and evaporation leads to decomposition
A reasonable first guess of the temperature where lava might evaporate is the approximate, known boiling points of alumina or silica (as Ivan Neretin's comment mentions). These are both close to 3,300 K (or C as the difference isn't much at such high temperatures).
There are problems with this estimate, though. Most lava isn't a pure compound but a mixture of one mineral with varying compositions or even a solution of many minerals of varying composition. Both of these considerations might alter both melting and vapourisation significantly. Worse, the vapour will not, in general, have the same composition as the liquid due to decomposition (minerals are often complex macromolecular mixtures containing large networks of silicate and aluminium oxides in varieties of infinite chains, panes or 3D structures which start to break up when liquid and certainty when in the vapour).
But this has been studied. This paper by NASA ("Vaporization and Thermodynamics of Forsterite-Rich Olivine and some
Implications for Silicate Atmospheres of Hot Rocky Exoplanets") studied the vapour pressure and composition of the common mineral olivine (a very common iron-magnesium silicate mineral). The vapour contains Fe, Mg, FeO, SiO, O and O2. This complicates any analysis. The experiments consisted of measuring the vapour pressures and composition of the vapour components above melted olivine at temperatures around the melting point.
However the paper provides a vapour pressure equation for the mineral that suggests the boiling point is about 3,700 K which is not outrageously different from the known values of SiO2 and Al2O3.
Other papers like this one "Critical vapourization of MgSiO3" (motivated by attempts to understand hot conditions after planetary collisions) have estimated critical liquid/vapour temperatures compatible with the estimate above.
So, a definitive answer is not possible as lavas are not all the same and the exact results are hard to measure directly. But estimates on some possible lava components and data from some pure compounds related to lava minerals have been done and suggest temperatures of vapourization of between 3,000 and 4,000 K at atmospheric pressure.