Does the dimmer you bought labeled as supporting LEDs? This Lutron TTCL-100H-WH does dim LEDs but this Lutron TT-300H-WH only dims incandescent and halogen bulbs. However, even if the dimmer supports LEDs, the transformer that came with the lights may not. The transformer (aka driver) I've used with LED lights (not Christmas lights) were labeled as "dimmable".

For a few years after they came out, it seems like many "120v" LED lights strings used the cheapest rectification (conversion to DC) imaginable. I remember maybe 7 or so years ago buying some strings at target that visibly flickered, even without dimming, and I returned them. It was infuriating.

The better quality sets are dimmable because they have better power supplies/drivers. You can probably find those at the big box stores, nowadays, but back 7 years ago I had to buy them from some internet retailers that focus just on lighting, like 1000bulbs.

So, you have to have strings of lights that accept dimming - they should say on the label - and a quality dimmer especially for LEDs, as wdccruise mentioned. Lutron is a great brand.