Free-volume structure of glassy lithium tetraborate Li2B4O7 is studied as compared with isocompositional crystal using positron annihilation lifetime spectroscopy in mixed positron-trapping and Ps-decaying modes exploring three-term decomposed positron lifetime spectra. The longest-lived lifetime component in Li2B4O7 glass is explained due to low-electron density spaces between neighbouring tetraborate groups, while second component is attributed to positron trapping in lithium vacancy-type complexes. Crystal-to-glass transition in free-volume structure of Li2B4O7 is examined with x3-x2-coupling decomposition algorithm. Assuming tight interconnection between atomic-deficient void structure of crystalline and glassy lithium tetraborates, the vitrification from crystalline state is described as expansion of positron-trapping complexes involving singly-ionized lithium vacancies in more spatially-extended positron-trapping sites, this being accompanied by large number of Ps-traps appeared preferentially in boron-oxide network of tetraborate structural units.