guitar imitating lap or pedal steel

If you're referring to guitars held perpendicular to the player's body, played with finger picks and a steel bar, then you would be mistaken to think they are imitating a lap or pedal steel. Those instruments are in fact imitating the original lap style acoustic guitars made popular by Hawaiian artists in the early 20th century. Most notable are the National and Dobro brands of instruments. Both emerged before the onset of electric amplification and implemented aluminum resonator cones which are essentially acoustic amplifiers. National guitars are known for their more rustic, tinny sound which tended to show up more in blues recordings. In addition to the resonator cone, Dobro implemented a spider bridge, which allowed for a more robust, bell like tone, a stark contrast to the tone deadening biscuit bridge used by National. The Dobro was a mainstay of country music during the 1930s and 40s, and then became a staple of bluegrass beginning in the 1950s. Some of the most notable artists of the Dobro guitar are Pete Kirby (better known as Bashful Brother Oswald), Josh Graves, Tut Taylor, Mike Auldridge, Jerry Douglas, Rob Ickes, Phil Leadbetter, Gene Wooten, Sally Van Meter, Stacy Phillips, Curtis Burch and Andy Hall. Their styles range from old time country and bluegrass to blues, jazz and a very progressive fusion of all of thee above. Hope that's what you were looking for.