Pertaining to weightlifting, the Multifidus counteracts forces in the sagittal plane whereas the iliocostalis lumborum counteracts forces in the frontal plane. Multifisus also is used as a synergist of the TrA during cocontraction to increase spinal segmental stabilization.
Multifidus 'condition' or dysfunction
results in less activity of Multifidus muscle at unstable levels during concentric back activity and decreased muscular protection at the hypermobile segment. In English, you would have (usually) bad to chronic back pain and hitting the weights would be difficult.
But lower back pain isn't necessarily or often multifidus probs.
If you have multifidus probs, low impact exercises are part of the rehab but not really pumping heavy weights. Its not my specialty so best ask a Chiro or someone though.