Q.We cut our lavender back fairly hard (not into the wood) hoping it would thicken up.
We shaped our very spindly lavender in early Spring, in the hopes that it would grow back thicker and with bigger flowers. It was cut back very neatly into a box shape and were very pleased with ourselves! Well, it has since grown back like a weed and its around 3 ft high (and wide), with tiny flowers, just turning lavender. What did we do wrong? Hope you can see what I mean?

Too much nitrogen will have this effect, as will not enough phosphorus. Avoid a high nitrogen fertilizer during flowering, or raise the pH of the soil a little with dolomitic lime.
This article will help: https://www.gardeningknowhow.com/edible/herbs/lavender/lavender-in-the-garden-information-and-growing-lavender-tips.htm