I think you might be looking for "tail" to get the last line of the file
e.g.
tail -1 /path/file
or if you want the last entry from each day then "sort" might be your solution
sort -ur -k 1,2 /path/file | sort
- the -uflag specifies only a single match for the keyfields will be returned
- the -k 1,2specifies that the keyfields are the first two fields - in this case they are the month and the date - fields by default are separated by white space.
- the -rflag reverses the lines such that the last match for each date will be returned. Sort a second time to restore the original order.
If your log file has more than a single month of data, and you wish to preserve order (e.g. if you have Mar 31 and Apr 1 in the same file) you can try:
cat -n tmp2 | sort -nr | sort -u -k 2,3 | sort -n | cut -f 2-
- cat -nadds the line number to the log file before sorting.
- sortas before but use fields 2 and 3, because field 1 is now the original line number
- sortby the original line number to restore the original order.
- use cutto remove the line numbers and restore the original line content.
e.g.
 $ cat tmp2
 30 Mar - Lorem Ipsom2
 30 Mar - Lorem Ipsom1
 31 Mar - Lorem Ipsom1
 31 Mar - Lorem Ipsom2
 31 Mar - Lorem Ipsom3
 1 Apr - Lorem Ipsom1
 1 Apr - Lorem Ipsom2
 $ cat -n tmp2 | sort -r | sort -u -k 2,3 | sort | cut -f 2-
 30 Mar - Lorem Ipsom1
 31 Mar - Lorem Ipsom3
 1 Apr - Lorem Ipsom2