There is not a typical or standardized work environment for a lyric writer. As mentioned above, many lyricists are freelance writers, and many of them work from home. It is also possible to rent out a studio space or office suite where you have a dedicated work area. This may help your concentration, as well as your professionalism when meeting with possible clients. It may be difficult to afford a rented office space when first getting started, but it would be a good thing to keep in mind for the future.