As others noted, if you do not have the lines of fixed width, it is impossible to do without building the index. However, if you are in control of the format of the file, you can get a ~O(log(size)) instead of O(size) performance in finding the start line, if you manage to store number of the line itself on each line, i.e. to have the file contents look something like this:
1: val1, val2, val3
2: val4
3: val5, val6
4: val7, val8, val9, val10
With this format of the file, you can quickly find the needed line by binary search: start with seeking into the middle of the file. Read till the next newline. Then read the line, and parse the number. If the number is bigger than the target, then you need to repeat the algorithm on the first half of the file, if it is smaller than the target line number, then you need to repeat it on the second half of the file.
You'd need to be careful about the corner cases (e.g.: your "beginning" of the range and "end" of the range are on the same line, etc.), but for me this approach worked excellently in the past for parsing the logfiles which had the date in it (and I needed to find the lines that are between the certain timestamps).
Of course, this still does not beat the performance of the explicitly built index or the fixed-size records.