TLDR;
The Lily system appears to be pretty useless. There is no reason to go out of your way to generate lilies in combat. WHM's lack of utility makes it a less than ideal choice for content that could be ideal for generating lilies. Even if you do manage to generate lilies, it is likely to provide little, if any benefit.
Explanation
My initial impression of the Lily system is that it is going to offer very little, if any benefits to WHM for 3 reasons:
Healing Downtime
This game has quite a bit of healing downtime in most content.
If your options are:Overheal is the worst and most wasteful option in the list. There really is no reason to actively try to build a stack of Lillies during combat. For the 'pure heal' healers, overhealing wastes MP and generates unnecessary enmity. For the veteran DPS oriented healers, building lilies via cure I and cure II is a dps loss.
- Deal Damage
- Do Nothing
- Overheal
No Raid Utility
While it's probably not a good ideal to try to build lilies during combat, savage content could potentially be designed in such a way to warrant substantial amounts of cure I & IIs for lily generation. However, WHM's lack of raid utility and AST buffs have made WHM a less than ideal choice for endgame content.
Healing in FFXIV is more about timing than HPS
As mentioned earlier there does not appear to be any reason to actively try to build lily stacks during combat. However, let's assume for the sake or argument that we are in content wherein the inbound dps is designed in a way that will allow the WHM to build Lilies.
When impacting a skill with a 1 min cooldown:
* the 1st lily: 2.4sec recast reduction
* the 2nd lily: an additional 3.6 second reduction
* the 3rd lily: an additional 6 second reduction
Basically, if you use a 1min cd with 3 lilies, you must use that cooldown again within 6 seconds of it becoming available, to have gained any benefit from that 3rd lily. In a game where using the right skill at the right time is essential... this is a pretty narrow window. Will I need cooldown X exactly 48-54 seconds from now? You could always burn a skill like assize for the damage + MP or tetra to save a cure II cast I guess... but in the end this lily system becomes a weak MP management system that is likely to only be somewhat useful in content that is better suited for AST.