1850 census of Morgan Co., Ky, enumerated 8 Sep, lists on pp. 107-108, as family #699:
Jackson Elliott, 34, laborer; Elizabeth, 38; Allen, 13; Cornelius, 10; William, 8; James, 7; Richard, 5; Milbourn, 5. All born in Kentucky.

Allen is unlikely to be a son of Jackson and Elizabeth, since they were married in July 1839. He may be a son of Jackson by a previous wife, but he may be a foster child. It appears that in 1860 he was listed with the surname Lewis, see below.

The next household is headed by Jackson’s father James Elliott Sr., age 79, with his second wife Mary, age 55, both born in Va.

1860 census of Morgan Co., Ky, district 1, enumerated 24 July, West Liberty P.O., lists on p. 91 as family #566/560:
Jackson Elliott, 45, farmer; Elizabeth, 49; Cornelius, 20; Robert, 19; James, 18; Richard, 17; George M., 15; Elihu, 8; Alexander, 5; John, 4; Allen Lewis, 22. All born in Kentucky.

There is no ditto mark for surname after Allen Lewis. This, combined with the fact that he is is listed out of age order, suggests that Lewis is his surname rather than a middle name. But he is probably the same person listed as Allen Elliott age 13 in the 1850 census.

Notice that Richard and George (Milbourn), who were recorded as the same age in 1850, are now recorded as two years apart.