The generic file read nodes in Node-RED do not, I believe care about individual lines, they just read the whole file.
I don't think the node.js fs library will pull an individual line either. However, there are certainly node.js packages that will probably do what you want - linereader for example? Look on npmjs.org.
This section of the Writing Functions page tells you how you can use the new FunctionExternalModules feature to pull in external code to use in a Function node.
It does, but then I get errors for "require" not being defined and stuff like that.
I'll play with it again on Saturday when I go back to work. I'll probably end up just writing and calling a Python script to get the data I need. I'd have been done with this a long time ago had I done that in the first place.
You can add require to the globals using the settings.js file. Then you can do a global.get('require') at the top of your function node.
Of course, as colin points out, you can require things in function nodes without going through that now if you are using the latest version of Node-RED.