For me I feel like the lilies need more ways of being obtained besides just Cure I/II. This alone would buff the whole mechanic tremendously.
-Cure I/II 20% chance per cast
-Regen 5% per tick of healing done.
(Could even go another step further and include AoE)
-Medica I/Cure III 5% or 10% per player healed
-Medica II 5% on initial cast and 2% per tick done per person.
And to help with avoiding just having hots up/spamming cure for funsies they could make it so that the target has to be under 100% when the tick/heal is applied (tho personally id prefer they didn't do this to Cure I just to allow a non damaging way to farm lilies outside of combat/so cure I spammers don't get too upset lol). Allowing regens to proc lilies also doesn't punish players DPS'ing so long as they at least have a regen up.
Personally from there I'd change the benefits of the lilies to give the next oGCD used an additional effect or just customize the lily procs per ability.
Like maybe instead of Divine Benison being a flat 15% no matter how many lilies maybe it goes up depending on the lilies you expend (15%/18%/20%) or maybe (12%/15%/18%) This even gives a nod to the original Stoneskin trait that made it from 10% to 18%.
Assize could get a buff Dmg/Healing Potency wise depending on the lilies you expend. 300 potency to (400/500/600) potency or maybe even restoring more MP.
Tetragrammaton could get a (50/75/100) potency regen attached to it depending on the lilies used up.
Asylum personally I can only think of giving it a cooldown reduction or (this might be a tad over powered) it could also increase the healing done to those inside itor flat out increase the Mind stat of those inside it or just the WHM that casted it. Might be a bit much, but with WHM's Divine Veil getting put into Cross Role, having this would not only give them another option for themselves already in their kit, but also could help their Co-healers giving some raid utility.
I mean I like the base idea of the lilies and I understand them wanting WHM to be a pure healer, but it defiantly needs some fine tuning and buffing to help it stand out. I mean the lily mechanic suffers the same issues mechanically wise as the Spear Card and Old Insta-cast Benefic procs seeing as though most folk will be planning and timing out when they use these cooldowns/heals. Shaving off a handful of seconds (or up to 12-19 seconds if you hold off casting an oGCD long enough to rack up 3 lilies) is okay I guess, but doesn't feel very active or appealing which is a tad disappointing especially when looking at SCH's fairy tether heal or AST's card gauge/new cards.
Thinking about the Benefic/Cure I procs, maybe the % chance doesn't need to be that fine tuned but I still think it should also be applicable for their other spells besides Cure I/II simply to discourage only using Cure I/II.