You are referring to Distributed Trunking (HP/HPE/Aruba aggregation technology well described here): so dt-trunk and dt-lacp options are like, respectively, trunk and lacp options for trunk command (where trunk means aggregate two or more physical links together) BUT those options (dt-trunk and dt-lacp) refer to a Distributed Trunking scenario.
Do not confuse trunk with the meaning Cisco gave to the word (basically tagging more VLAN IDs on the same interface).
Edit: for the very same reason that dt-trunk option is different by dt-lacp option (exactly like trunk option is not like lacp option) I suspect the Switch 4 (top Access Switch 2520 in the presentation linked above, page 45 of 60) configuration line:
Switch4(config)# trunk 3-4 trk4 lacp
is wrong, it should have been instead:
Switch4(config)# trunk 3-4 trk4 trunk
The example (top Access Switch versus bottom Access Switch, both uplinked to a DT depolyment of two HP 5412zl switches) was provided to highlight the fact you can have Non Protocol Trunks and IEEE 802.3ad (LACP) Trunks that are terminating into the DT deployment.