1.  Ohio, County Marriages, 1789-1994 (online at familysearch.org):

Groom's Name:	Hezekiah Lynch	Elmer E. Lynch	Elmer E. Lynch
Event:	Marriage	Marriage	Marriage
Event Date:	30 Jul 1863	25 Jun 1891	24 Nov 1910
Event Place:	Hardin, Ohio	Logan, Ohio	Logan County, Ohio
Groom's Age:			45
Groom's Father:			Hezekiah Lynch
Groom's Mother:			Lenna Andrews
Spouse:	Lavina Osbun	Libbie Iams	Mina Fry
Spouse's Age:			36
Spouse's Father:			James Mulligan
Digital Folder / Source Film:	914828	4284781	4260459

2.  1870 U.S. Census Every-Name-Index/Images (online at Ancestry.com):  Elmer E. LYNCH (æ 6, b. OH) is living in Hale Twp., Hardin Co., OH (p. 392A), with his parents, Hesakiah LYNCH (æ 29, OH) & Luvina (æ 29, b. OH).

3.  1880 U.S. Census Every-Name-Index/Images (online at Ancestry.com):  Elmer E. LYNCH (æ 16, b. OH) is living in Mt. Victory, Hardin Co., OH (p. 85D), with his parents, Hezekiah LYNCH (æ 41, VA) & Levina (æ 41, b. OH).  Elizabeth P? IAMS (æ 8, b. PA) is living in Rushcreek Twp., Logan Co., OH, with her parents (q.v.).

4.  1890 U.S. Census:  the 1890 Census Population Schedules were destroyed.

5a.  1900 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #6 of 15):  South High [St./Ave.], Mount Victory, Hale Twp., Hardin Co., OH, Roll 1284, p. 69B, SN 2, SD 7, ED 85, enumerated 2 Jun 1900, official enumeration date 1 Jun 1900 (extracted by Diana Gale Matthiesen):

1900:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	19	20	22	23	24	25	26	27	28
74	77	Lynch Hesikiah	Head	W	M	Feb 1838	62	M	37			VA	VA	VA	Farmer	0	Y	Y	Y	O	F	F	4
		Lavinia	Wife	W	F	May 1838	62	M	37	4	3	OH	PA	PA			Y	Y	Y
		Elmer E	Son	W	M	Apr 1864	36	*				OH	VA	OH	Physician	0	Y	Y	Y

I can't decipher Elmer's marital status; someone put a "W" over something else.  Back then, there was such a stigma associated with being divorced, it's not uncommon to see a divorcé (or divorcée) giving their status as widower (or widow).

5b.  1900 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #27 of 34 — indexed "Jams"):  Main Street, Rushsylvania Village, Rushcreek Twp., Logan Co., OH, Roll 1294, p. 254A, SN 14, SD 7, ED 123, enumerated 21 Jun 1900, official enumeration date 1 Jun 1900 (extracted by Diana Gale Matthiesen):

1900:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	19	22	23	24	25	26	27
290	296	Iams Thomas	Head	W	M	Jul 1833	66	M	45			PA	PA	PA	Retired	Y	Y	Y	O	F	H
		____ Lydia	Wife	W	F	Dec 1833	66	M	45	7	3	PA	PA	PA		Y	Y	Y
		Lynch Elizabeth	Dau	W	F	Mar 1873	27	M	9	1	1	PA	PA	PA		Y	Y	Y
		_____ Leota	GDau	W	F	Jul 1892	7	S				OH	OH	PA

6.  1910 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #4 of 12):  Ridgeway, Hale Pct., Hardin Co., OH, Roll T624_1187, p. 91B, SN 2B, SD 7, ED 103, enumerated 23 Apr 1910, official enumeration date 15 Apr 1910 (extracted by Diana Gale Matthiesen):

1910:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1	2	3	4	5	6	7	8	12	13	14	17	18	19	20	23	24	25	26	27	28
15	15	Lynch Elmer E	Head	M	W	45	Wd	OH	VA	OH	Eng	Physician	Druggist	OA	Y	Y		O	F	H
		_____ Leoti	Dau	F	W	17	S	OH	OH	OH	Eng				Y	Y	Y

7.  1920 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #26 of 26):  Mt. Victory Village, Hale Twp., East Pct., Hardin Co., OH, Roll T625_1397, p. 155A, SN 14A, SD 7, ED 91, enumerated 28 Jan 1920, official enumeration date 1 Jan 1920 (extracted by Diana Gale Matthiesen):

1920:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).

2

3

4

5

6

7

8

9

10

11

12

16

17

18

19

21

22

23

24

25

26

27

28

X

230

230

Lynch Dr E E

Head

O

M

M

W

56

M

Y

Y

Ohio

Ohio

Y

Phronician?

General Practice

OA

_____ Mina

Wife

F

W

48

M

Y

Y

Ohio

Ireland

Irish

Ireland

Irish

Y

None

Frye Everat

Son

M

W

20

S

N

Y

Y

Ohio

Ohio

Ohio

Y

None

Everett is our subject's stepson, Mina's child from her prior marriage.

8.  1930 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #
 
 

10.  Directory of Deceased American Physicians, 1804-1929 (online at Ancestry.com):

Name:	Elmer Ellsworth Lynch
Birth Date:	25 May 1864
Death Date:	26 Jan 1929
Death Place:	Marion, OH
Type Practice:	Allopath
Licenses:	OH, 1896
Practice Dates Places:	Ridgeway, OH, 1896 Mt. Victory, OH, Jan 26, 1914 Marion, OH, Sep 30, 1920
Hospital:	Marion City Hosp.
Medical School:	Toledo Midical College, Toledo, 1895, (G)
JAMA Citation:	92:668
Cause of Death:	rheumatic arthritis

11.  Ohio Adjutant General's Office.  1926-29.  The Official Roster of Ohio Soldiers, Sailors and Marines in the World War, 1917-18. 23 vols.  F.J. Heer Printing Co., Columbus, OH (online at GenealogyLibrary.com and at Ancestry.com):

v. L, p. 10480

LYNCH, ELMER ELSWORTH, Capt., White, Mt Victory, O.

Br Hardin Co, O. Apr 25/64. 1 Lt MC Jan 23/18 fr ORC.  Capt Sept 12/18.  Mil Hosp 21 35 BH 208 to disch.  AEF.  AEF Mch 8/18 to June 24/19.  Hon disch Oct 9/19.

12.  Public Member Trees (online at Ancestry.com):

13.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).