Really? When has low unemployment ever caused inflation?
Yes, really. Too low of an unemployment rate (yes, there is such a thing) causes inflation. Meaning, employers can’t find people to fill the jobs, and, must compete for the (un)available labor by paying more and more. This reached a crescendo in 2000 when some high-tech companies were giving huge signup bonuses and BMWs for people to switch companies. We all know how that ended.
Ultimately higher labor costs are passed to the consumer, and, voila, there’s your inflation. Therefore, Fed will not be lowering rates any time soon - if anything, they’ll be wanting to raise rates as labor markets overheat.