Megan S. answered 11/18/20
Patient and Knowledgeable Multi-Subject Tutor and Mentor Team
So, the short answer to your question, assuming we are speaking about two cisgender women, is "No, not yet."
As you said, since cisgender women do not produce sperm, the sperm has to come from a third party. So although reciprocal IVF, where one woman carries the pregnancy but they use the other woman's egg, is possible, donor sperm would still be required. With reciprocal IVF, technically the egg of one of the partners is growing in the other woman's womb, so pre-birth environmental factors would be provided by that mother's womb, giving that mother a pre-birth influence on the child's development, despite the lack of genetic relation.
Technically, you could have the donor be someone related to the woman who is not producing the egg. (Like a brother or a cousin.) Then the baby would have some genetic similarities to both moms. But this isn't quite the same as being related directly as a parent.
And of course, regardless of who the baby is genetically related to, or who carries the baby, both moms would have an impact on the child's development after birth by influencing the child's environment and the way it is "nurtured", just as we see with adoptive straight parents.
But this is the state of things right now.
There is currently work being done to figure out if somatic (non-sex) cells can be converted to gametes (eggs or sperm). It is called IVG and has been done successfully in rats, though not humans yet. This could potentially allow same-sex couples to have children fully genetically related to both of them. https://www.statnews.com/2019/06/05/creating-eggs-sperm-stem-cells/
Also, there have been "three parent babies" created in rare, controversial circumstances, in which the genes from two eggs are mixed before being crossed with sperm. https://nationalpost.com/news/canada/dr-john-zhang
The main thing is that once you get into messing with the genetics of a baby, conversations are going to spring up everywhere about "slippery slopes" and genetically engineered "designer babies", and the truth of the matter is, we probably could use some degree of regulation on how far the genetic determination of a baby can go before we all go nuts with it, though this is not to say it's a bad idea overall. There is also the issue of trying to ethically test this out with big enough sample sizes in human subjects samples to be certain that babies born through this method do not have any unintentional genetic issues caused by the not-as-yet-perfected process. Of course, the positives are that for same-sex couples and people struggling with infertility issues or severe genetic disabilities they don't want their children to inherit, these technologies would be revolutionary.
So. In summary, is it possible for cisgender lesbians to both be the biological parents of their children someday? Yes. We are getting there. But is this happening much as of now? No. Not yet.