The Lightning Network (LN) does not have its own blockchain. Payments in the LN use native Bitcoin transactions for payments.
To create a LN channel, two users put funds into a shared address. Before submitting the funding transaction to the blockchain, they exchange Bitcoin transactions which would allow either party to reimburse the shared funds to the respective owners. These commitment transactions are valid Bitcoin transactions that the channel owners could submit to the Bitcoin network at any time to close the channel and reclaim unencumbered ownership of their funds. While a channel operates as intended, the commitment transactions remain unbroadcast—they only serve as a fallback.
When one LN user pays another, the sender kicks off a series Bitcoin transactions which have users forward a payment along a route through the LN. Each of these transactions put a Hash Time Locked Contract (HTLC) on a portion of the funds of the forwarding channel to ensure that the forwarded funds do not get spent in another way. When the payment settles, the channel operators fold these HTLCs back into the channel’s balance by replacing the previous commitment transactions.
As you can see, the Lightning Network acts as a caching layer or compression mechanism for regular Bitcoin transactions. While it does not have its own blockchain, it is heavily reliant on the availability of the Bitcoin blockchain to resolve disputes and guarantee existence of funds.
I’ll leave up to you whether that fits your definition of “blockchain technology”.