Oh, boy! Time for a math lesson.
lumens is a measure of total light output. lux is a measure of how much light falls in a (small) area.
Given a candle (or something similar) with no focusing, light goes equally in all directions. Therefore, at a distance of 2 meters, the light hitting a given area (of the inside of the 2-meter radius sphere) is 1/4 that of the light hitting the same area on a 1-meter sphere, because the total surface area is 4 times as large and the total amount of light is the same. Therefore, when measuring lux, it's necessary to give the distance from the source.
If a light were focused to a pinpoint, it would be possible for a .01 lumen light to measure 100 lux at that pinpoint (and 0 lux outside it). Two lights might have the same amount of lumens, and the focused one a lot more lux; or the same lux, and the unfocused one a lot more lumens.