It's ... built-in. It's just not line completion, because, you're saying it, it's not an entire line you want to complete.
If we start from your example:
; A sentence I would like to auto complete.
...
A sentence|
If I now press C-n, followed by C-x C-n (secret sauce! - context completion) it will complete the following word. Press C-x C-n repeatedly to further complete the next words. If it doesn't work, try it from a vim -N -u NONE and go from there.
You should probably use a more complex example, one that have multiple variants, e.g.:
; A sentence I would like to auto complete.
; A sentence you don't like to complete.
...
A sentence|
In this case, when you hit a "branch" with options (e.g. I or you), you should select the continuation you want using the usual C-p / C-n keys, then go on with C-x C-n as before.
You can find the docs at :h i_CTRL-X_CTRL-N, in the 2nd part (quoted, for reference):
CTRL-N Search forward for next matching keyword. This
keyword replaces the previous matching keyword.
CTRL-P Search backwards for next matching keyword. This
keyword replaces the previous matching keyword.
CTRL-X CTRL-N or
CTRL-X CTRL-P Further use of CTRL-X CTRL-N or CTRL-X CTRL-P will
copy the words following the previous expansion in
other contexts unless a double CTRL-X is used.
<eol>? – jecxjo May 05 '16 at 16:27<eol>. – s3rvac May 05 '16 at 18:18