It is well-known that lipids constituting the cytoplasmic membrane undergo continuous reorganization to maintain the appropriate composition important for the integrity of the cell. The transport of lipids is controlled by mainly membrane proteins, but also spontaneous lipid transport between leaflets, lipid "flip-flop", occurs. These processes do not only occur spontaneously under equilibrium, but also promote structural rearrangements, morphological transitions, and growth processes. It has previously been shown that intravesicular lipid "flip-flop" and intervesicular lipid exchange under equilibrium can be deduced indirectly from contrast variation time-resolved small-angle neutron scattering (TR-SANS) where the molecules are "tagged" using hydrogen/deuterium (H/D) substitution. In this work, we show that this technique can be extended to simultaneously detect changes in the growth and the lipid "flip-flop" and exchange rates induced by a peptide additive on lipid vesicles consisting of DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine), d-DMPC (1,2-dimyristoyl-d54-sn-glycero-3-phosphocholine), DMPG (1,2-dimyristoyl-sn-glycero-3-phospho-(1'-rac-glycerol)), and small amounts of DMPE-PEG (1,2-dimyristoyl-sn-glycero-3-phosphoethanolamine-N-[methoxy(polyethylene glycol)-2000]). Changes in the overall size were independently monitored using dynamic light scattering (DLS). We find that the antimicrobial peptide, indolicidin, accelerates lipid transport and additionally induces limited vesicular growth. Moreover, in TR-SANS experiments using partially labeled lipid mixtures to separately study the kinetics of the lipid components, we show that, whereas peptide addition affects both lipids similarly, DMPG exhibits faster kinetics. We find that vesicular growth is mainly associated with peptide-mediated lipid reorganization that only slightly affects the overall exchange kinetics. This is confirmed by a TR-SANS experiment of vesicles preincubated with peptide showing that after pre-equilibration the kinetics are only slightly slower.