As always, I love world building questions which try to explore some novel approach to life, only to find that nature has already found a way. It's marvelous what nature can do.
Lamarkian evolution actually does happen, to some degree. While much of our genetic evolution is very Darwinian, there are plenty of example of extended phenotypes which get inherited from the mother in utero. Many traits of a child find their origins in mother's choices while pregnant. Your baby's sense of taste, for example, gets partially developed from the mother's diet. Live in a part of the world where eating garlic is essential for life? Your child will actually pick up a taste for garlic from the amniotic fluid it lives in, long before it ever sees the bulbous herb.
Perhaps a love of garlic isn't exactly a life skill, but other traits that operate this way are very valuable. For instance, it has been found that a baby reacts to mother's stress hormones in utero. If mommy has found that the only way to cope with the harshness of life is through the stress hormones like cortisol (which tune the body to face the stress), the baby will develop to generate more cortisol in stressful situations and decrease cortisol slower after the stress is removed. This has actually been measured, correlating maternal cortisol levels during pregnancy to cortisol levels produced during the baby's first blood draw.
Sound harsh? Maybe not. One of the known effects of cortisol is a decreased immune system, and worse allergic reactions. These sound useless right? Maybe not. Biochemically, it suppresses outputs of Th1 helper T cells, while activating Th2 cells to encourage them to produce more output. As it turns out, Th1 cells are primarily involved in fighting bacterial and viral infections. Th2 is more involved with our defense against extracellular parasites like worms. Now we don't have many worms in our modern 1st world life, so we don't benefit much from Th2 upregulation. However, if you are living in a part of the world where worms and other parasites are a regular part of life, this response is very useful.
So we have an example of Lamarkian evolution, at least at an extended phenotype level. If mother deals with a lot of worms in her life, her cortisol levels will tend to be higher. The child will then develop accordingly, and be born more ready to deal with the infectious world around them than they would have been if mom didn't stress her body. And likewise, if the baby is a girl, it is likely that her stress levels will be passed to the next generation.