We use three dimensional optical spectroscopy observations of a sample of 22 local Luminous Compact Blue Galaxies ( LCBGs ) to create kinematic maps . By means of these , we classify the kinematics of these galaxies into three different classes : rotating disk ( RD ) , perturbed rotation ( PR ) , and complex kinematics ( CK ) . We find 48 % are RDs , 28 % are PRs , and 24 % are CKs . RDs show rotational velocities that range between \sim 50 and \sim 200 ~ { } km~ { } s ^ { -1 } , and dynamical masses that range between \sim 1 \times 10 ^ { 9 } and \sim 3 \times 10 ^ { 10 } ~ { } M _ { \odot } . We also address the following two fundamental questions through the study of the kinematic maps : ( i ) What processes are triggering the current starbust in LCBGs ? We search our maps of the galaxy velocity fields for signatures of recent interactions and close companions that may be responsible for the enhanced star formation in our sample . We find 5 % of objects show evidence of a recent major merger , 10 % of a minor merger , and 45 % of a companion . This argues in favor of ongoing interactions with close companions as a mechanism for the enhanced star formation activity in these galaxies . ( ii ) What processes may eventually quench the current starbust in LCBGs ? Velocity and velocity width maps , together with emission line ratio maps , can reveal signatures of Active Galactic Nuclei ( AGN ) activity or supernova ( SN ) driven galactic winds that could halt the current burst . We find only 5 % of objects with clear evidence of AGN activity , and 27 % with kinematics consistent with SN-driven galactic winds . Therefore , a different mechanism may be responsible for quenching the star formation in LCBGs . Finally , from our analysis , we find that the velocity widths of RDs , rather than accounting exclusively for the rotational nature of these objects , may account as well for other kinematic components , and may not be good tracers of their dynamical masses .