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Are there any romance dramas where the male lead has some sort of disability {physical or disease) like Boku no ita Jikan (ALS) or Aishiteiru to Ittekure (deafness) while the female lead tries to help him deal with the problems. This causes problems in their relationship as they try and deal with it.

Would love if there's a love triangle where a douchey 2nd guy who likes the female lead and tries to use the guy's disability to tear them apart.

I want a happy ending.

Kill me Heal me
Can you hear my heart
It's okay that's love
Kimi ni Sasageru Emblem
Koe Koi
Koizora

I have several Disability and Illness lists on my Profile. 

Disabilities: Autistic, Blind, Crippled, Deaf, Intellectual, Mute, Misc
Illnesses: Brain Tumor, Cancer, Dissociative Identity Disorder, Heart Condition, Neurodegeneration, Schizophrenia, Various

I can't make any specific recommendations for what you're looking for, but having some titles to browse through may help. :)
Try this Dear My Friends.
The romance is not the main or integral part of story overall, but still important part of the woman's main lead story. The male character had an accident that causing his disability to walk.

And this It's Okay That's Love.
The main male lead has mental issues, dealing with his traumatic past. Super romance, and super recommended by me.
I forgot to put that I want happy endings.

@Neyjour - Looking for more physical disabilities/diseases rather than mental ones.

@fanitha & iamgeralddd - I'll check them out and see if anything interests me. Thanks.
 Algernon ni Hanataba o ---> male lead has a mental disability
Autumn's Concerto ---> male lead gets amnesia
Beautiful Life ---> female lead has a physical disability
Love Song ---> female lead stutters 
Ohh I just saw that you mentioned happy endings!....don't watch Algernon or Beautiful Life then..
If you don't mind a movie suggestion....Hear Me and also drama special Myu no Anyo Papa ni Ageru
Itoshi kimi e is exactly what you're looking for! (Except I don't remember if there's any second male lead.)