This paper is dedicated to investigating the kinematic properties of the Lupus moving group of young stars with the primary objective of deriving individual parallaxes for each group member. We identify those stars in the Lupus star-forming region that define the comoving association of young stars by utilizing our new and improved convergent point search method that allows us to derive the precise position of the convergent point of the comoving association from the stars' proper motions. We used published proper motion catalogs and searched the literature for radial velocities, which are needed to compute individual parallaxes. We supplemented the radial velocity data with new measurements from spectroscopic observations performed with the FEROS spectrograph mounted on the MPG/ESO 2.2m telescope at La Silla. We identify a comoving group with 109 pre-main sequence stars and candidates that define the kinematic properties of the Lupus low-mass star-forming region. We derive individual parallaxes for stars with known radial velocity and tentative parallaxes for the remaining group members by assuming that all stars share the same space motion. The convergent point method, combined with the k-NN algorithm, makes it possible to distinguish the Lupus and Upper Centaurus Lupus stars from the adjacent Scorpius-Centaurus association. We find significant depth effects in this region and show that the classical T Tauri stars, located in the close vicinity of the Lupus molecular clouds, form a background population, while the weak-emission line T Tauri stars are dispersed not only in angular extent but also in depth. The newly derived individual parallaxes will be used in a forthcoming paper to refine the masses and ages of Lupus T Tauri stars, with the aim of better constraining the lifetimes of their circumstellar, protoplanetary disks.Read less <