What counts as a technical replicate and what as a biological replicate is not a fixed thing and depends on what your statistical question is and how generalizable you wish to be.
For example let us consider a single gene: gene A and cell types: parent and derived. I'm going to take as if we are interested in a one-tailed result (gene A is greater in derived than parent), but the following applies equally to the one-tailed less than case and the two-tailed case.
If you take multiple aliquots of the same library as your replicates then you are asking: "Are there definitely more reads from gene A in the library from the derived cells than the parent cells". You do not need replicates for this question. We know what the distribution of repeated sampling from the same library should be.
If you take multiple libraries prepared from cells in the same dish as your replicates you are asking: "Do cells in this dish of derived cells definitely have more gene A than cells from that dish of parental cells. We generally regard repeated library preps from the same source material as reproducible enough that this can be modelled as above.
If you take your dish of derived cells and split it into three plates, grow to confluence and then prepare libraries you are asking: "Do cells from this derivation event definitely express more gene A compared to the parental line?"
If you taken your dish of parental cells, split it into six dishes, grow to confluence and then derive in three of those dishes you are asking the question: "Do cell derived from this dish of parental cells definitely have more gene A than the cells which were not derived?"
If you were to take three separate sets of the parental cell line from different source and derive each of them you are asking: "Is gene A always unregulated when I derived cells from this cell line?". Here different source could mean purchasing triplicate aliquots from ATCC or it could mean defrosting separate aliquots from your own freezer.
If you took cell lines derived from three different people with the same cancer, and performed the derivation on each one you are asking: "Is gene A always upregulated when stem cells are derived from this cancer?"
If you were to take 3 different parental cancer cell lines from different cancers and derive each one you would be asking: "Does deriving stem cells from cancer cell lines definitely lead to an upregulation of gene A?
What you should do probably depends on how difficult and time consuming the derivation is. The ideal compromise is probably to defrost 3 separate aliquots of HepG2 cells, and perform the derivation of each line three times.
However if the derivation is the sort of thing that is going to take you six months and $1000s to do, then there might be an argument for taking three aliquots of cells from the same derivation, growing them to confluence and using these as your replicates.Just remember that if you do this, the claim you can make of the result is "This is how RNA levels changed when we derived stem cells" NOT "This is how RNA levels change when stem cells are derived from HepG2 cells" (in general).
Replicates from the same cell line often show very little variation, and so in the second case you are likely to get a large number of genes as significant. That is, many genes DID change when you derived stem cells. However, that list will not necessarily be very reproducible if you did the derivation again, and definitely not so reproducible if you did the derivation on a different hepatic cancer cell line.