L2/L3 aren’t UTXOs, which also means they wouldn’t control keys.
Discussion
I have keys for Zeus wallet which has L1, L2 and L3. Also software like Muun allows lightning txs and UTXOs with swapping.
Going strictly by your first note, you’d be gifting dust. I don’t know your level of understanding of UTXOs, so was just trying to help out in case you didn’t know they’d probably be dust. “Their own keys” typically implies self custody UTXOs onchain, not blended, pseudo custody of L2/L3 LSPs, VTXOs, ecash, etc.
I also really appreciate the sentiment of gifting like that to grandkids, it’s an admirable dream.
Gotta have some dreams (I have too many).
When the time comes I’ll weigh options and see what’s most economical and feasible.
Will be interesting to see if a 10,000 sat UTXO will be viable in 20 years.