The Insteon 2477D dimmer is officially rated for incandescent lighting only. However we've seen many people successfully use Insteon dimmers with LED lighting. The 2477D is a leading edge electronic dimmer.
There are many LED bulbs that are sold as compatible with dimmers. In reality the quality of dimming, and how low they will dim before starting to flicker or cause issues is partly related to the quality and electronics inside the LED bulb itself. Ideally the bulb will need to be compatible with leading edge electronic dimmers. If in doubt contact the LED manufacturer.
If you try a dimmer compatible LED bulb and your results aren't great, we suggest trying another brand or two to see if you can find one that is more truly designed to work with this type of dimmer. If your LED lighting is using a separate transformer, your electrician may know of a transformer that will work well with this type of dimmer.
Ultimately, on/off switches like the 2477S are fully compatible with LED lights but of course you can't dim them when used with this on/off switch.
We hope that Insteon will one day release a dimmer that they will stand behind as supporting LED lighting completely. But in reality we have seen that other brands such as Zwave dimmers, even when they are designed for LED lights specifically, produce poor results with some bulbs and manufacturers so some trial and error on the bulbs may be in order even in this case.