When culturing my mESC feeder-free on Biolaminin 511 or Biolaminin 521, do I have to add LIF to prevent the cells from differentiating?

No, Biolaminin 511 and 521 supports self-renewal of mouse ES cells in the absence of feeder cells, LIF, or other differentiation inhibitors, even at low cell density. Both laminin isoforms successfully support both naive and primed stem cells since it has been shown to activate the PI3/Akt pathway while the MAPK/ERK pathway is unaffected (Rodin et al., 2014).