When I started writing, I was in the same boat as you. I had all the left-brain skill, but the right-brain creativity was more difficult, even though I always considered myself more of a creative, altruistic person. This is how I started.
Write about something that is near and dear to your heart, or something that really speaks to you. Using descriptive words are good, as well as imagery (words that relate to the senses). Try picking a topic, brainstorming a list of words that pop into your head when you think of that topic, and then write the music. Listen to the music while you're in the lyric-writing process, to fuel your thought. My music theory teacher gave us that advice when we were composing a piece for an end-of-the-year project, and mine came out really really well using that process.
Or, pick a memory of something that really stands out to you, and take some quiet time to sit in silence & dwell on that memory. Think of every possible thing-what it looked like, what people were there, if any, what time of day it was...ANYTHING and EVERYTHING. Then, freely write a poem. It doesn't have to be any kind of structure or sequence, just write about the memory. Then write your music while you're still in that zone. After that, try to match key words and phrases in a rhythmic pattern to the music, and presto.
Hope this helped-both methods work for me!