I mostly write using a word processor (LibreOffice at the moment) and I use tabs to indent lines so that I know what beat of the bar a line of lyrics begins at.
To polish my lyrics, I use Rhymesaurus. It's found at...
http://www.purpleroom.com/rhymesaurus-for-windows/I find this software an incredibly powerful tool (and a great buy for US$12.95)
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I mostly use Rhymesaurus for...
1. Finding rhymesMostly I stay with the "Perfect" and "Assonance" rhyme options. (See the first image below.)
2. Finding alliterationAs an example... if I want a three syllable word beginning with H that has the primary stress on the first syllable, I set Rhymesaurus as shown on the second image below.
3. Finding better wordsFor this I use the Thesaurus feature. What I like about this is that words are also internally linked so that navigating through a train of thought or a particular concept becomes easy.