Underrealm Lich's first ability is a replacement affect that turns your draws into a very Sultai/Golgari themed choose a card and fill the graveyard effect.
Yes, Gaea's Blessing will trigger
701.15b Revealing a card doesn’t cause it to leave the zone it’s in.
701.15d Some effects instruct a player to look at one or more cards. Looking at a card follows the same rules as revealing a card, except that the card is shown only to the specified player.
Revealed cards are considered to be in the zone they were revealed from. Therefore, when Underrealm Lich's ability causes you to look at cards and then put them in the graveyard, they have moved from the library to the graveyard, triggering Gaea's Blessing.
Yes, if you put Gaea's Blessing into your graveyard using Underrealm Lich's ability, Gaea's Blessing's ability will trigger and you will shuffle your graveyard into your library.
Gaea's Blessing's ability says
When Gaea's Blessing is put into your graveyard from your library, shuffle your graveyard into your library.
And Underrealm Lich's relevant ability says
If you would draw a card, instead look at the top three cards of your library, then put one into your hand and the rest into your graveyard.
So, at any point where you would draw a card, instead you perform the instructions in Underrealm Lich's ability. If Gaea's Blessing is among the cards you look at and you choose to put it into your graveyard, then it will move from your library to your graveyard so its ability will trigger.