Can I add a logical partition to a filesystem with an LVM?
 

If I deleted /dev/sda4? I wasn't aware of the 4 primary partitions per disk limitation, and I need to be able to have 4-5 more partitions on this disk that would all eventually be added to the LVM. I'm not sure if the LVM itself counts as the one allowed logical partition per disk.

Here is a cfdisk screenshot of the partition table:

http://tinypic.com/view.php?pic=28v6rrn&s=6

a primary partition is a primary partition, there's no interest in what the partition type is (and note that this "limitation" is a 100% DOS legacy issue, Linux doesn't care at all.

LVM partitions can be primary or logical, it's just seen as a block device at the level LVM deals with it at.

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.