[PamConnell]

Ribby--
I adopted internationally and haven't faced this situation, and I'm not a counselor--just a writer specializing in writing about adoptions. Some of my blogs here on the Families.com site deal with "children's tough questions" or telling children tough topics like abandonment, etc. Not exactly relevant, but may be somewhat helpful.
My gut says you've done all the right things--continuing to communicate but not forcing yourself on the bmom, and asking what she wants to do given her situation.
Respecting the bmom's rights is paramount, of course, but I would gently urge her to help create some memories and/or information for your daughter to have, now or later. Perhaps you could ask her if she could, while she feels well enough, make a simple audio tape or video of herself speaking a few words to your daughter.
If she does visit or have you visit her, I would encourage all the adults to think of it more as visiting a family member or relative they haven't seen--tell her honestly that it's her birthmother whose tummy she grew in, but don't keep stressing "L's mother is dying". She might begin to fear you will die, or perhaps fear that the visit is to return her to her birthmother. Adoptive families who visit their child's home state or birth country are often advised to schedule a family trip or activity right after the visit trip, to reinforce that your nuclear family is not changing. Some general children's books about death may be helpful here--a librarian can probably recommend some.
Brenda Romanchik has published a book--whose title eludes me now--a book similar to a "baby book" designed for a birthparent to fill out for her birth child--er interests, hobbies, school struggles and strengths, etc. Perhaps you could send one to L's bmom and hope she fills it in for her.
You seem to be doing all the right things so far--hang in there.
It is important that you try to find out exactly what type and variation of cancer the birthmother has and what age she was when it first occurred. You or the intermediary should urge her to provide at least this much information for your daughter's future.
You may also try to find out where your daughter's half-brothers may be living and try to set up contact, through the intermediary if necessary, so that all the bmom's biological children can exchange medical information later.