If I respawn a boss and kill him with Lucatiel again, does that count towards the 3 bossfight requirement to prevent her from disappearing

In order to reverse the hollowing you need to use the Human Effigy (like you would use a lifegem), not burn it at a bonfire. This means you're able to use the item anywhere, and can save them for right before a difficult boss fight.

As of Patch 1.03, you'll regain a small portion of humanity for helping other players:

Players now receive a small portion of Humanity after successfully assisting in a Multiplayer session instead of regaining full Humanity.

Finally, there is a way to increase your maximum HP when Hollowed:

! The Binding Ring will ensure your maximum health can't go lower than 75% when hollowed. You find this ring in The Cathedral of Blue, right before entering the fog gate. It'll be in a chest to your left at the top of the drawbridge. If you are playing Scholar of the First Sin, then the earliest Binding Ring can be found in Heide's tower of flame right before the dragonrider boss fight, there is a Heide's Knight sitting in front of a chest, tackle him and you will receive the ring from opening the chest.

Human Effigies can be found from Starting Gift, Static Locations (corpses), Merchants (All merchants have limited supply), and NPC's (both given and dropped when killed).

The term 'farm' usually implies an unlimited resource, as you pointed out. As of the latest patch, the Company of Champions covenant allows infinite respawn.

These are enemies that drop Effigies:

• Attack Dogs.
• Skeletons [not in Undead Purgatory]
• Turtle Knights.
• Sentinel (Sword/Shield) and Sentinel (Great Sword)

Always remember you can farm 6 effigies off of the Old Firekeepers and 3 alone off Housekeeper Milibeth in Things Betwixt.

After unlocking the Shrine of Winter, it is possible to farm Smooth and Silky Stones. While not directly farming Effigies, these have a high conversion rate to Effigies at Dyna & Tillo (Drop trade crow), although this is random.

There is however a way to restore humanity consistently.

In the Shrine of Amana, above the last bonfire, there is a Shrine with a praying Milfinito. After you have 'rescued' the two stray maidens (one outside the Demon of Song room, another behind the Embedded Door in Drangleic Castle) you can pray at this Shrine at any time to regain humanity. This is free of cost and can be done a limitless amount of times.

There is an easier way, although it seems so easy that it will be patched.

This requires the Ring of Life Protection, which can be found at the No Man's Wharf. This ring prevents loss of your Humanity and souls on death, but breaks afterwards. This ring can be repaired for 3000 at the blacksmith giving a constant 3000 Souls per Human transfer rate. A +1 Ring of Life Protection (Also prevents petrification) can be purchased from Vengarl in the Shaded Woods.