The 1786 Westmoreland County Tax list is quite revealing! Here we find the Applegate's, Peter Lanterman, and Jeremiah Nesbit; all directly connected to David/John Lindsay!

See also the "Jersey Settlement" & the Applegate pioneers!

Westmoreland County PA Archives Tax Lists - 1786 Septennial Census - Westmoreland County

Armstrong   Viz            100
Rostraver`                 384
North of Hempfield         157
South of Hempfield         29x
Derry                      211
Mount Pleasant             335
North Huntington           203
South Huntington           204
Pitt                       350
Wheatfield                  31
Fairfield                   57
Donnegal                   107
              Total       2509

Rostraver Township

              A

Applegate Benjamin Sr.		
Applegate Benjamin single
Applegate Garrard
Applegate Richard  (Father of Aletta Applegate re: wife of Peter Lanterman; mother of Sophia Lanterman Lindsay)
Applegate William
Applegate Robert  single
Applegate William  Do
Applegate Daniel 
Applegate  Jonathon single
Applegate Samuel
Applegate James

            L

Little Samuel    (Later found in Fleming County, KY and went to Sangamon County, Illinois with the Lantermans and John Lindsay.)

Lowry John
Linn John
Lane James 
Lowry Stephen
Lemon Thomas
Lemon Henry
Lemon Samuel  single
Larjeant Nelson Do
Lappin Elizabeth
Lemon Joseph
Lanterman Peter		(Father of Sophia Lanterman Lindsay)

Larimore Samuel single
Long Benjamin

South District of
Huntington

          L

Lindsey Hezekiah		(Reported brother of David Lindsay, apparently untrue!)
Long William
Latta Ephraim
Light Jonathon
Logan Thomas
Latta William Sr.
Light Peter
Loughhead Joseph
Latta William
Lewis Ezekiel
Leonard James
Lodge Benjamin
Lattimore George

        N

Neely Mathew
Newell Margaret
Nesbit William
Nesbit Jeremiah		(Signed Ruddle's Mill Petition with David Lindsay)
Norris George		See
Nyman Harman
Newell Hugh		Hugh Newell reportedly married Elizabeth McNay; had 10 children; Son William married Isabel Lindsay;

		                 in 1799 at Harrison County, KY. [See]              
Newell Robert

We can see that Peter Lanterman is found in Westmoreland County as early as 1782:

The Pennsylvania State Archives published 10 series of historical records (138 volumes) covering the initial colonial settlement through the Civil War.
Series: Series 6
Volume: II
Chapter: Battalions Not Stated Westmoreland County Militia.
Page: 344

The Pennsylvania State Archives published 10 series of historical records (138 volumes) covering the initial colonial settlement through the Civil War.
Series: Series 3
Volume: XXII
Chapter: Transcript of Property with Number of Inhabitants in the County of Westmoreland, 1783.
Page: 375