Lycius is an uncommon Greek name (e.g., a character in Keats's poem Lamia).  "Lycius" would appear to be the name clerks were trying to spell, though he may simply have been, Lucius.

Parents possibly…
Father:  Thomas STROUP / STROPE, Sr.
Mother:  Ann? __?__

1a.  Anon.  1966.  Marriage Index:  Ohio, 1789-1850.  Liahona Research, Orem, UT (Broderbund CD-400):

Tucker, Lysin R.

Strope, Lovina

30 Jun 1842

Lorain Co.

1b.  LDS.  Family Search: Internet Genealogy Service:  IGI - International Genealogical Index (online at FamilySearch.org).

Lysine R. TUCKER Spouse: Lovina STROPE Marriage: 30 Jun 1842, Lorain, Ohio Source: Marriage Records, 1824-1932. Ohio. Probate Court (Lorain County)

I'll wager "Lysine" is a mis-reading of Lysius or Lycius.

2.  1850 Census Index/Images (online at Ancestry.com; Image #4 of 18):  Greenfield Twp., Erie Co., PA, Roll M432_777, p. 77B, 33/34, enumerated 1 Oct 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):¤•

Lysias Tucker	30	M		Mill Wright	500	NY
Lovina   "	26	F				Penna
Henry    "	6	M				Ohio
Zylphia  "	5	F				"
Eliza    "	3	F				"

3.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #14-15 of 30):  Grafton P.O., Grafton Twp., Lorain Co., OH, Roll M653_1002, pp. 251B-252A, PN 138-139, 1001/1026, enumerated 20 Jul 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):¤•

Lucius Tucker	46	M		Millwright		350	New York
Lavinia	38	F					Penn
Henry	16	M					Ohio
[next page]
Silpha Tucker	14	F					Ohio
Eliza	12	F					"
Mary	9	F					"
Jane	2	F					"

4.  1870 Census Every-Name-Index/Images (online at Ancestry.com, Image #13 of 33):  LaGrange P.O., LaGrange Twp., Lorain Co., OH, Roll M593_1235, p. 549A, PN 13, 108/111, enumerated 18 Jul 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):¤•

Tucker Licius	52	M	W	Miller		300	NY
______ Lovina	46	F	W	Keeping House			Penn
______ Eliza	24	F	W				Ohio
______ Mary	18	F	W				NY
______ Jane	11	F	W				Ohio
______ Wilmot	8	M	W				Ohio
Lispinller Willie	7	M	W				Ohio
Tucker Henry	27	M	W	works in Grist Mill			Ohio
______ Maggy	25	F	W	Keeping House			Germany
______ Unnamed	1/12	M	W				Ohio	May

5.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #16 of 50):  Johns Street, Wellington Corporation, Lorain Co., OH, Roll T9_1042, p. 643D, PN 16, SD 16, ED 183, enumerated 8/9 Jun 1880, official enumeration date 1 Jun 1880 (extracted by Diana Gale Matthiesen):

1880:  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

8

9

10

13

21

24

25

26

194

199

Tucker Henry

W

M

36

/

works in Planing Mill

OH

OH

OH

"   Maggie

W

F

34

Wife

/

Keeping House

Ger

Ger

Ger

"   Charlie

W

M

10

Son

/

At School

/

OH

OH

Ger

"   Ada

W

F

5

Dau

/

OH

OH

Ger

"   Ray

W

M

3

Son

/

OH

OH

Ger

"   Ann E

W

F

28

Sis

/

At home

OH

OH

OH

"   Willie

W

M

19

Bro

/

works in Planing Mill

OH

OH

OH

Is Ann E. actually Mary?  Or is she Eliza and telling a big fib about her age?

6.  1890 Census:  the 1890 Census Population Schedules were destroyed.

7.  Andrew W. Young.  1875.  History of Chautauqua County (online at the Chautauqua County NYGenWeb site):  The only reference I've found, anywhere, to a "Lysias TUCKER" is in this book, listed as an early pioneer in Mina, Chautauqua Co., NY.