Is Lena's father's illness an excuse?
Apparently Lenas (step-)dad has cancer and is in remission?
I'd believe it would be hard to fake cancer and the treatments have noticeable side-effects, like e.g. his complete baldness. I am not familiar how much medication and medical care is actually needed while in remission, but compared to an ongoing therapy fighting acute cancer it should be way less.
Lenas dad had to sell his bakery due to his illness and seems to be partially disabled since then. He never recovered his old strength and isn't working full-time or at all. Lenas mom does a subpar job to cover for it and her brother is apparently also useless in that regard.
So it looks to me like her parents problem at the moment is mainly stemming from the income side than the expense side of their household budget.
While it is true, their current predicament is indeed based on his illness, i actually don't feel like there is enough effort from especially her mother and her brother to ease the situation. It's just not fair to rely to that degree on their also struggling daughter, who had to give up her college education already and is now working two jobs as a waitress, while her mother doesn't.
(...) Do you think such behavior on their part as "milking Lena" is normal and justified?
This would depend very much on their cultural background and the country they would live in. In most parts of the world, people have to rely on their families, because they have a non-existent social security system.
I can't recall if it is ever mentioned in which country ORS takes place, but from the mainly white cast with a rather high percentage of characters from other ethnic backgrounds it's imo safe to say it's either western europe, canada or the USA. The dominance of english given names point to either Great Britain (however i would expect at least one south-asian character there), or Canada or the USA.
While in the USA such behaviour may be normal and justified, i'd feel like not so much in the other two countries.
MyLena feels obligated to contribute, but only if her own situation allows spending money on her family. Thus myLena skipped at least one payment, but transferred money on other occasions.