Just about every reputable source rejects Lysenkoism, belief in the transmission to offspring of environmentally acquired traits.
This less reputable source suggests a potential pathway for such transmission.
Perhaps my suggestion is not pure Lysenkoism, but I will describe it anyway.
Besides DNA, other things may affect the developing fetus. Nutrition and circulating hormones affect brain development, and may cause activation or deactivation of genes. At certain times, it will be more sensitive to the environment of the womb. The health and actions of the mother affect that environment. Ill health or stress at critical junctures can severely affect the growing child.
Imagine a stress prone mother. She is always worried and anxious; pregnancy makes this even worse. Large amounts of stress hormones circulate in her body. The fetus lives in an environment soaked with these stress hormones. The stress hormones affect the developing brain, turning on certain genes, causing enlargement of the growing amygdala. Eventually a young baby girl enters this world, sharing her mother’s nervous disposition.
This young girl grows up, and so becomes a mother herself. Wanting to ease the stress of pregnancy, she takes up yoga. The yoga calms her; her circulating stress hormones decline to normal levels. Her unstressed body now provides better nutrition to her growing baby girl. The lack of stress hormones means certain genes are no longer activated, the amygdala grows to normal size. Eventually a young baby girl enters this world, lacking her mother’s nervous disposition.
In this case, an environmental change was transmitted to the offspring. Or maybe I am very wrong. Medically or genetically minded readers can discuss.
Even if my description were correct, it would mean that only the mother could transmit such traits.
Even if correct, the genotype remains the same. However, the yoga mother’s child will likely not bathe her own daughter in the stress hormones, and thus the trait could effectively become part of the germ line.
This is more fun thought experiment than an attempt to forge a new theory. It is not that I reject my own theory; it is just that I have no basis to know how likely or unlikely, how sensible or silly, it is.