When on blood pressure meds, what herbal supplementation for sleep cause possible problems?

First of all when you start taking supplements you must inform your DR. of every single one you are adding to your treatment, that being said, the following supplements do not interact with Lisinopril and Chlorthalidone:

Chamomile, click on the link for the interaction report:

https://www.drugs.com/interactions-check.php?drug_list=2357-0,642-0,1476-0

Valerian Root does interact with alcoholic beverages and it would not be wise to combine them:

https://www.drugs.com/interactions-check.php?drug_list=642-0,1476-0,2284-10628

The following herbs interact potentially negatively with Chlorthalidone:
dandelion, uva ursi, juniper, buchu, cleavers, horsetail, and gravel root.

"Herbs that have a diuretic effect should be avoided when taking diuretic medications, as they may increase the effect of these drugs and lead to possible cardiovascular side effects. These herbs include dandelion, uva ursi, juniper, buchu, cleavers, horsetail, and gravel root."

This is why it is so important that you inform your Dr. on all the herbal supplementation you are on.