LED dimming is a compatibility mess. Most commercial buildings don't use 2-wire dimming where you're messing with the sine wave on the hot wire for dimming, instead they give you a clean 120V circuit and tell you the dimming level over some other channel (whether it's wireless, 0-10V analog, or some digital bus), and these tend to perform a lot more consistently. But most residential equipment doesn't work that way because houses don't have the additional wiring for it, so we're stuck with 2-wire.
When you get into 2-wire dimmers where it's chopping up the sine wave to reduce power, everything gets sloppier. The only 100% reliable strategy to avoid problems is buying LED bulbs that have been tested on your specific dimmer system.
Consumer products are especially frustrating because a lot of time the technical specifications are missing important information like whether it's for forward phase or reverse phase dimming. That relates to which end of the sine wave gets chopped off for dimming, and they don't play nicely with each other. Reverse phase is the more common these days, but it doesn't hurt to confirm.
EDIT: I should note that if you're looking at screw-in LED light bulbs you want to search "A Lamp". Bit of industry jargon, we measure things in 1/8 inches (because reasons), so what normal people consider a standard lightbulb is an "A19 lamp" meaning A-series with 19/8" (2.375") diameter.
To put it more simply still; AC light dimmers work by 'turning off' the sine wave part way through the cycle. This works on purely resistive loads (light bulbs) and blows up motors (ceiling fans).
LEDs are direct current devices that run on less than 2V. So they convert the electricity coming in to DC, then regulate it down to their voltage. No amount of 'sine wave chopping' is going to dim them.'
As a result they try to cheat, they try to both convert AC to DC and to measure the incoming sine wave and guess that it is being dimmed by an old style dimmer.
In the GP comment, the engineer chose perhaps poorly. Clearly as soon as power is available the light comes on full, then after the 'dim' setting is measured it adjusts the light level to the 'dim' setting.
What the light might do when it receives power is first do the measuring to look at the sine wave. then after it knows what brightness it is being commanded to show, then enable the LEDs. Now how long does it wait? If it waits 16mS (or 20mS for 50hz) then it can see a 'full' cycle. But since it could start anywhere it really needs to wait 24mS/30mS because that way it is sure to have at least one full cycle in its memory. However, if there is a 'smart' dimmer (think X-10) involved it may just pass through unclipped sine waves as it powers up because "the incandescent light takes many milliseconds to warm regardless." If the LED waits longer before it turns on you cross 100mS which is where pretty much everyone would note a 'lag' between turning on the light and actually having it come on.
All of that just to that a 20 year old dimmer based on TRIACs still works as 'expected' by the user.
Another lingo note, the old-school TRIAC dimmers are the forward phase ones. Being mostly on the commercial side I don't see much of this, but maybe on residential products that's what's implied when something calls itself "dimmable".
When we get 2-wire dimming it's usually reverse phase (AKA Electronic Low Voltage (AAKA ELV)).
When you get into 2-wire dimmers where it's chopping up the sine wave to reduce power, everything gets sloppier. The only 100% reliable strategy to avoid problems is buying LED bulbs that have been tested on your specific dimmer system.
Consumer products are especially frustrating because a lot of time the technical specifications are missing important information like whether it's for forward phase or reverse phase dimming. That relates to which end of the sine wave gets chopped off for dimming, and they don't play nicely with each other. Reverse phase is the more common these days, but it doesn't hurt to confirm.
Lutron does a fair bit of compatibility testing and lists their recommended products here: http://www.lutron.com/en-US/Service-Support/Pages/Technical/...
EDIT: I should note that if you're looking at screw-in LED light bulbs you want to search "A Lamp". Bit of industry jargon, we measure things in 1/8 inches (because reasons), so what normal people consider a standard lightbulb is an "A19 lamp" meaning A-series with 19/8" (2.375") diameter.