I have managed to record the leveling-up of a regular Artisan Goblin Worker and the leveling-up of an Artisan Goblin Worker with Blessed Hand skill.
I would like to compare how their luck has changed.

Regular Artisan Goblin Worker

Luck on character sheet before: 11.21
Luck on character sheet after: 11.32
Difference: +0.11
Luck on Cotton Wool work node before: 12.21
Luck on Cotton Wool work node after: 12.72
Difference: +0.51

Artisan Goblin Worker with Blessed Hand skill

Luck on character sheet before: 11.98
Luck on character sheet after: 12.45
Difference: +0.47
Luck on Coal work node before: 11.98
Luck on Coal work node after: 12.45
Difference: +0.47

The character sheet result is straightforward. The node result is not what I was expecting. The regular Artisan Goblin Worker has a Lucky Guy A skill, which affects node luck (he had the same 12.72 when doing Coal as when doing Cotton, so the two types of gathering node seem to be the same for luck). What's strange is the Lucky Guy A skill seems to give a bigger boost upon leveling up than even the Blessed Hand skill! Well, as it turns out, regular Artisan Goblin Worker became level 35, and by trollish chance, gained a Lucky Guy C skill, throwing our results off kilter.

Regular Artisan Goblin Worker, adjusted for Lucky Guy C acquisition upon level

Luck on character sheet before: 11.21
Luck on character sheet after: 11.32
Difference: +0.11
Luck on Cotton Wool work node before: 12.21
Luck on Cotton Wool work node after: 12.32 (12.72 - 0.04 = 12.32) 
Difference: +0.11

Artisan Goblin Worker with Blessed Hand skill

Luck on character sheet before: 11.98
Luck on character sheet after: 12.45
Difference: +0.47
Luck on Coal work node before: 11.98
Luck on Coal work node after: 12.45
Difference: +0.47


So the results are that the Blessed Hand worker gained 0.36 more luck than the regular worker (0.47 - 0.11 = 0.36). This is more than the advertized +0.2. Perhaps luck gain is subject to randomized raises. We won't know from the data I have, but perhaps someone else can share their data, or I can add to it once more workers level up.

Source screenshots in reply post.

Elion's blessings,
Felana Nafonia

I logged a Blessed Hand Human Worker leveling up. Luck increased from 26.05  to 26.37, a +0.32 change. This is different from the +0.47 luck when the BH Goblin leveled up in the earlier post. It bolsters my hypothesis that luck gain is randomized.