Flow/Rhyme. The lyrics you have written should flow, and an easy way to make them flow is to contain some sort of rhyme pattern and some internal rhymes. Of course, I think the rhyme patterns should be original and should deviate from the norm as much as possible. Be original. Experiment with rhyme schemes.
Analogies. Now, sometimes little or no editing to the initial draft may be needed, but a lot of the time various changes are required. When writing you could make this your mantra: "heart leads head". On occasion, you may write about something tragic that happened in your life, but none of the grief or devastation will connect with the reader/listener. This is probably due to the fact that you got too sentimental in your words, and forgot that others may not be able to feel the emotion, due to the simple fact that your words are words and nothing more. For a writer to paint pictures with words he will need to make connections, and to do this he will need to use either similes or metaphors. The picture will then be interpreted differently by each reader/listener and most will find a different emotion in it. This is why metaphors and similes, when used correctly, can create truly wonderful lyrics.
Styles -
Find a style for you. Obviously thoughtful lyrics tend to be provocative and their main aim is to make the reader/listener think. Then there are emotional lyrics, which try to make the listener feel. For further explanation on both of these types of lyrics go here. Then there are the two different styles of lyrics, which of course are literal and metaphorical. As for metaphorical lyrics, there is one thing to be wary of: do not write lyrics that contain an abundance of metaphors, because in truth, they'll come out in an unintentionally confused manner, and most of the ideas will become redundant.
The Initial Draft. Let yourself relax so that you're in a frame of mind where the words are flowing and coming out naturally. People can tell when you forced yourself to write, (in your early days of writing anyway). Also, don't think that rhyming is an absolute necessity. If you write something, which sounds okay to you, then don't ruin the lyrics by putting in unnecessary rhymes. Don't get technical, don't worry about flow, and don't try to rhyme. You can do all these things when editing. The most important thing is that you express yourself, and hold nothing back. This is your time, imagine no one else can hear you, speak your mind, and be completely open.