It's hard to know exactly what name was intended for Dicey.  The given name, "Laodice," is found in Greek mythology (e.g., a daughter of Priam of Troy) and was historically common as a given name among Greeks — and as a Greek place name under various spellings (e.g., it appears in scripture as Greek place name, "Laodicea").  Bottom line is that it was not an uncommon name in the South in the 19th-century.

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

Jonas STROUP Spouse: Rebeckah CLONINGER Marriage: 25 Nov 1821, Lincoln, North Carolina Source: patron submission

2.  1830 Census Index/Images (online at Ancestry.com, Image #159-160 of 214; extracted by Diana Gale Matthiesen):¤•

1830

NC

Lincoln [now Gaston] Co.

Roll 122

p. 233B-234A

Ln. 2

Jonas Stroup

310 001 - 110 001

no slaves

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
3 males	4 or under	1825-1830	= Son A = Maxwell (b. 1827/8) = Johannes (b. 1825/6)
1 male	5-9	1820-1825	= Rufus (b. 1824/5)
1 male	30-39	1790-1800	= Jonas (b. 1799/1800)
1 female	4 or under	1825-1830	= Daughter A
1 female	5-9	1820-1825	= Caroline (b. 1823)
1 female	30-39	1790-1800	= Rebecca (b. 1799/1800)

Listed one line below Moses STROUP, Jr. (æ 20-30), and one above Michael STROUP (æ 50-60), who is one line above Solomon STROUP (æ 30-40).  If I had to guess, I'd guess Jonas's father was Michael.

3.  1840 Census Index/Images (online at Ancestry.com, Image #75-76 of 84; extracted by Diana Gale Matthiesen):¤•

1840

NC

Lincoln Co.

Roll 364

pp. 137A-137B

Ln. 12

Jonas Stroup

022 100 100 - 211 101 000

no slaves

0501000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	5-9	1830-1835	= Cephas (b. 1831/2) = Wesley (b. 1830/1)
2 males	10-14	1825-1830	= Maxwell (b. 1827/8) = Johannes (b. 1825/6)
1 male	15-19	1820-1825	= Rufus (b. 1824/5)
1 male	40-49	1790-1800	= Jonas (b. 1799/1800)
2 females	4 or under	1835-1840	= Emily Frances (b. 1837/8) = Mary Rebecca (b. 1835/6)
1 female	5-9	1830-1835	= Dicy (b. 1834)
1 female	10-14	1825-1830	= Daughter A
1 female	15-19	1820-1825	= Caroline (b. 1823)
1 female	30-39	1800-1810	= Rebecca (b. 1799/1800)
5	persons employed in agriculture
1	person employed in manufactures and trades

4.  1850 Census Every-Name-Index/Images (online at Ancestry.com, Image #132 of 145):  Gaston Co., NC, Roll M432_630, p. 458A, 978/978, enumerated 14 Nov 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):¤•

Jonas Stroup	50	M		Mechanic	800	No Ca
Rebecca   "	50					"
Rufus     "	25	M				"
Johnce    "	24	M				"
Maxina    "	22					"
Wesley    "	19	M				"
Cephus    "	18	M				"
Loda Esco "	16	M				"
Mary R    "	14					"
Francis C "	12	M				"
Dorcas L  "	6					"

5.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #81 of 182):  Chenut Oak P.O., Gaston Co., NC, Roll M653_898, p. 41A, PN 81, 632/570, enumerated 17 Jul 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):¤•

Rufus Stroup	35	M		Farmer	1800	882	Lincoln
Rebecca  "	55	F					"
Diza     "	20	F					"
Mary     "	18	F					"
Dorcas   "	14	F					"

Listed next to married son, Maxwell STROUP (æ 33); and, in the other direction, listed four households from married son, "Johanan" STROUP (æ 32).

6.  1870 Census Every-Name-Index/Images (online at Ancestry.com):  Rebecca not found.

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