Thank you for your question about pruning your lavender.  Dead wood on lavender can be removed at any time.   

Lavender does respond well to pruning.  I have attached a link to an article from the Colorado State University Extension office, which describes how to prune lavender. This article states:

Lavender should be pruned every year after it is established.  Pruning should take place when green leaves start to emerge from the base of the plant in the spring.  Remove approximately one third of the top.  Pruning keeps the plant from splitting open and becoming too woody. 

https://extension.colostate.edu/docs/pubs/garden/07245.pdf

The Oregon Lavender Association suggests pruning lavender plants in the spring and summer, and then lightly in the Fall, helps the plants to grow better over a longer period of time.  Lavender plants that have not been pruned consistently may become woody looking sooner.  In general, all lavender will benefit from being pruned at least once a year.  Major pruning should be done in the spring and summer months.  You can find more information about pruning lavender at the following link:

http://oregonlavenderdestinations.com/pruning-lavender/

If you have more questions, or need additional information, please call the OSU Master Gardener Plant Clinic.  We welcome your home garden questions.  You can call and talk with the Master Gardener on duty at<personal data hidden>.  You can also submit questions with photos to the Master Gardener Plant Clinic email: <personal data hidden>.