Is it possible with Gedit or the command line to modify every fourth line of a text file?

You could use a command-line editor such as sed

sed 'N;N;N;s/\n/\t/g' file > file.tsv

or, more programatically, by adding backslash line continuation characters to each of the lines you want to join using GNU sed's n skip m address operator and following it with the classic one-liner for joining continued lines:

sed '0~4! s/$/\t\\/' file | sed -e :a -e '/\\$/N; s/\\\n//; ta'

See for example Sed One-Liners Explained :

39. Append a line to the next if it ends with a backslash "\".

    sed -e :a -e '/\\$/N; s/\\\n//; ta'
    

However IMHO itwould be easier with one of the other standard text-processing utilities e.g.

paste - - - - < file > file.tsv

(the number of - will correspond to the number of columns) or

pr -aT -s$'\t' -4 file > file.tsv

(you can omit the -s$'\t if you don't mind the output to be separated by multiple tabs).

---

The strange re-import behavior that you are observing is almost certainly because the original file has Windows-style CRLF line endings. If you need to work with files from Windows, then you can roll the conversion into the command in various ways e.g.

tr -d '\r' < file.csv | paste - - - -

or

sed 'N;N;N;s/\r\n/\t/g' file.csv

The former will remove ALL carriage returns whereas the latter will preserve a CR at the end of each of the new lines (which may be what you want if the intended end user is on Windows).

You can use xargs to always group four lines into one, separated with a single space each:

xargs -d '\n' -n4 < inputfile.txt

-d '\n' sets the input delimiter to a newline character, otherwise it would also break on spaces. If you only have one word per input line anyway, you can even omit this.
-n4 sets the argument number (the number of input items per output line) to 4.

Output:

Dog Cat Fish Lizard
Wolf Lion Shark Gecko
Coyote Puma Eel Iguana

Or if you want tabs as separators instead of a space, you can replace them afterwards. However, if you had spaces in your input lines, those would get replaced too:

xargs -d '\n' -n4 | tr ' ' '\t'

Output (look depending on browser/terminal's tab width):

Dog Cat Fish    Lizard
Wolf    Lion    Shark   Gecko
Coyote  Puma    Eel Iguana

My solution to this would be to use combination of sed and sed. First, you could mark every fourth line with some special character, for example >, using this solution:

• Adding a character to every other text line

In this case you want to start from line 5 and mark every 4th line after it. In GNU sed that can be given as an address 5~4. You can use this command:

sed '5~4s/^/>/' file1 > file2

Then you need to remove the newlines, which can be done with a sed loop:

sed ':a;N;s/\n/ /;ba' file2 > file3

There are easier ways to convert newlines to some other character, for example with tr:

tr '\n' ' ' < file2 > file3

Either way, combining the two gives

Dog   Cat   Fish   Lizard   >Wolf   Lion   Shark   Gecko   >Coyote   Puma   Eel   Iguana

(the sed version leaves a trailing newline, while the tr version does not)

After that, you need only convert the special characters you inserted to newlines; see for example Convert a tab-delimited file to use newlines. In this case, change > to newlines:

sed 'y/>/\n/' file3 > outfile

The y command performs the same function as tr, transforming one character into another, but you can use the s command here equally well. With s, you need g to operate on each match in the line (sed 's/>/\n/g').

Rather than making two intermediate files, you can use pipes:

$ sed '5~4s/^/>/' file | sed ':a;N;s/\n/ /;ba' | sed 'y/>/\n/'
Dog Cat Fish Lizard 
Wolf Lion Shark Gecko 
Coyote Puma Eel Iguana

If trailing spaces are a problem, you can add another command to remove them:

| sed 's/ $//'