Logerstedt is likely a spelling variation or Americanized spelling of Lagerstedt, a Swedish compound ornamental name derived from words describing natural phenomena that were used when surnames were adopted there in the late 1800's and early 1900's. (They were late bloomers, surname-wise!) Lagerstedt is a combination of lager and stedt, meaning literally "laurel homestead." Other Lager names along the same line (the first element lager = laurel) Lagerbach (stream), Lagerberg (hill), Lagerborg (town), Lagerkrantz (wreath), Lagerdahl (valley), Lagerfeldt (field), Lagerfors (waterfall), Lagergrehn (branch), Lagerquist (twig), Lagerlof (leaf), Lagerstrandt (shore), and Lagerstrom (river).
So Lagerquist means "laurel twig".