The lyonization process is reversed in Germline cells (of females) which are suspended in Prophase I of Meiosis, until puberty (and then you know what happens).
In somatic cells, the reversal of lyonization happens in the S phase, before mitosis and separation of the
chromosomes to each daughter cells. In the S phase, variations of levels of specific proteins called cyclins and association of these cyclins with a protein called Cdk2 (cyclin-dependent kinase) will cause the chromosomes to decondense fully and allow DNA replication by DNA polymerase. After G2 and mitosis, if the cell returns to a resting (G0) state, the same X sex chromosome (being paternal or maternal for a female or only maternal for the male) will recondense and form a barr body.
But.. this is too much info. Just know that it happens.
(And, yes, multiple professors CAN confuse you if they don't know what they're talking about, especially since the process CAN be irreversible in certain species, at certain stages, in certain tissues. A lot of what we know about genetics comes from animal experimentation.)