The paper Towards Bitcoin Payment Networks (thanks this answer for the link) gave me a clearer understanding of the topic. Here is a very simplified summary of what I've learned.
There are multiple approaches to payment channels, including:
- A simple uni-directional channel (replace-by-incentive);
- A simple bi-directional channel (with decrementing timelocks, i.e., replace-by-timelock);
- Duplex micropayment channels (see also: my related question);
- Lightning network.
In Lightning, a single bi-directional channel is constructed using a breach remedy transactions (BRT), the idea being: before updating the channel state, both parties commit that if they broadcast an earlier state, the counterparty will be able to claim all funds. This is achieved with relative timelocks.
Furthermore, Lightning channels are connected into a network, where payments can be routed through non-custodial parties. This construction is based on hash time locked contracts (HTLC). The receiver generates a random value R, sends H(R) to the sender, and the sender specifies in the output script that R is requires to claim it. After the transaction propagates through nodes, the ultimate receiver discloses R and claims their funds; knowledge of R, in turn, allows all parties along the route to claim their funds from the previous node. In order to give each party time to do so, decrementing absolute timelocks are used.
Summary: the Lightning network does not use decrementing timelocks in a single channel, but uses them in multi-hop channel networks.