I am definitely not a healer main, but when I heal I use white mage. I thought I would share my thoughts about changes to strengthen white mage while also trying not to tip balance to hard. There are only two abilities I would change to bring improvement.

free cure: make Stone/Glare the ability that procs free cure. Doing some unnecessary math, since we all already know cure fishing is bad, a 15% proc means you cast cure seven time per proc, granting 3500 potency, costing 3500 MP to get one free 800 potency heal. The cure power of cure II is nearly equal for half the GCDs, 3200 for four cure II's costing 4000 MP. The situations you need heal spam is pretty much only trash pulls, and cure wont keep the tank alive. You pretty much never (or should never) cast cure once you have cure II. This will fix some of the MP problem since you get free cure for spamming glare, which you already were doing.

Lily: I want to compare lily to the other healers special resource heals.
AST has no special resource heal, it instead has cards which can be kept on CD, additionally AST heals cost a less MP. This is the least comparable to lilies but the difference is the card CD can always be ticking.
SCH using aetherflow, a 60 second CD granting three charges and restores 20% MP, you can also hold your charges and let the CD tick, letting SCH use up to six 600 potency heals on a 1 second recast in rapid succession. CDs also tick while dead, making little downtime aetherflow, but lilies and addergall reset to zero if you die.
SGE gets addersgall, which they get every 20 seconds and spend for a 600 potency heal and a 7% mp restore on a 1 second recast. This ability recharges faster, recasts faster, restores MP, and you are always generating stacks.
While WHM gets 1 lily every 30 seconds only while in combat (the timer also resets if combat ends if I'm not mistaken) for a 700 potency heal on a full GCD recast.
How I would fix this is recharge every 20 or 30 seconds (depending on how often Devs want blood lily to activate) in and out of combat like SGE and shorten the recast to 1 second to match SGE and SCH heals.

Side topic: Lots of players are saying, using the blood lily is a potency loss over glare spam. I do not think the potency of 4 GCD glare, vs 4 GCD for one blood lily is comparable. You can only blood lily once every 90 seconds when you get 3 lilies (36 GCD), and you glare/dia/heal 33 times between every blood lily. So really its a potency gain, because you will have to stop the glare spam to heal during actual play. Yes if you are just doing a DPS test, blood lily is a damage loss, but in practice you should be spending lilies anyway so I do not think it needs a potency buff or really any change, especially if lilies generate in and out of combat.

Regardless of blood lily, lilies are inferior to the special resource heals currently being used by the other healers, both in how long it takes to get your stacks, and how quick you can spend them.