Chris' comments are true, but need some elaboration to answer the (largely implied) question.
In future, how about you ask the entire question in the post, instead of starting it in the subject ?.
Note your unusable area - if you delete sda4, you will wind up with a larger area that must (in this case) be allocated as a primary partition. That can be configured as a pv, and added to the LVM vg.
Ugly but workable.