Hi, 

This looks like a perennial speedwell, a cultivar of Veronica spicata maybe. Lavender would have a distinct smell and the flowers and foliage would be different. The foliage is more of a fine cut leaf and has a silvery grey color on most varieties. and flowers generally are a lighter medium to lighter purple. 

You can do an internet search for "Veronica spicata, purple flowers" and you will get various results. It could be a hybrid variety as well as there are different Veronica species. 

Emily

Thank you, Emily!