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".

From http://www.4crests.com/surmeanio.html