Not quite. Lumen is a measure for how much light is emitted, lux says something about how much light arrives at a specific point - so lumen is (kind of) looking at the source, while lux is looking at the 'target'.
In the context of a lamp, lux only really means something when combined with a distance. 100 lumen is 100 lumen no matter what you point the lamp at, as that's just the amount of light it emits - 100 lux however might be measured at 1m distance, or at 100m distance, and it makes a very big difference in terms of what kind of light you'd need for that.
Not quite. Lumen is a measure for how much light is emitted, lux says something about how much light arrives at a specific point - so lumen is (kind of) looking at the source, while lux is looking at the 'target'.
In the context of a lamp, lux only really means something when combined with a distance. 100 lumen is 100 lumen no matter what you point the lamp at, as that's just the amount of light it emits - 100 lux however might be measured at 1m distance, or at 100m distance, and it makes a very big difference in terms of what kind of light you'd need for that.
See this handy image:
Note how 500 lumen translates to only 28 lux at 10m distance in their example.