Dmitri, your solution is actually pretty compact and straightforward. The only thing more efficient would be to keep the string-splitting characters in the generated array, but the APIs simply don't allow for that. As a result, every solution will require iterating over the array and performing some kind of modification (which in C# means allocating new strings every time). I think the best you can hope for is to not re-create the array:
string[] lines = tbIn.Text.Split('\n');
for (int i = 0; i < lines.Length; ++i)
{
lines[i] = lines[i].Replace("\r", "\r\n");
}
... but as you can see that looks a lot more cumbersome! If performance matters, this may be a bit better. If it really matters, you should consider manually parsing the string by using IndexOf() to find the '\r's one at a time, and then create the array yourself. This is significantly more code, though, and probably not necessary.
One of the side effects of both your solution and this one is that you won't get a terminating "\r\n" on the last line if there wasn't one already there in the TextBox. Is this what you expect? What about blank lines... do you expect them to show up in 'lines'?