The occurrence of octupole shapes in even-mass neutron-rich Ba isotopes has been well established. However, the situation with the odd-mass Ba and odd or odd-odd La nuclei around them is not so clear. In order to shed light on these less-studied isotopes, a fast-timing experiment was performed using the GRIFFIN spectrometer at TRIUMF-ISAC. A wealth of excited-state lifetimes in the 100 ps to few ns range have been measured in Ba144,145,146 and La145,146 populated in the β- and β - n decay of Cs145,146. The results do not allow one to draw firm conclusions about the possible octupole deformation of these nuclei but suggest different spin and parity assignments than previous works. This work highlights the need for more detailed study of the odd and odd-odd isotopes in this region to properly understand their structure.