This happened to me too, with an Actiontec MI424WR rev D router with DD-WRT. (Recently updated via its web-interface to "actiontec-mi424wr-firmware.bin", r42872 (20200410), which is the newest one that doesn't fail to update (files 7564MiB or larger don't "take"; this is a separate problem).)
I inserted the MI424WR between my PC and my existing (other-brand, stock firmware) router, and tested it heavily (a few days and many megabytes via wired and wireless). Then I went to install it elsewhere, to replace someone's very old router. Not once did it get an IP address from the modem via DHCP. I cloned the MAC address of their old router; no DHCP. I tried giving it, as a static IP address, the same address (and netmask and DNS servers) that the old router received via DHCP; no Internet access. I replaced their 11-year old ISP-provided Arris modem with a new ISP-provided Arris modem. Still nothing. Back home, it is almost the same. I installed the MI424WR between my PC and my 2-year-old ISP-provided Arris modem, and it seemed to get an IP address from the modem just once, and lost it. But when I connected my old router back to the modem, and inserted the MI424WR between my PC and the existing router (again, like I tested it), it took a few more restarts than I expected, but it works fine (again). (I am connected that way right now.)
I don't know what I am missing. Maybe I didn't leave the modem OFF long enough. Maybe I didn't wait long enough after powering up the modem before powering up the MI424WR.
Maybe the modem tracks more than just MAC; maybe I have actually to call the ISP to flip the "secret bit". But my ISP is very permissive about MAC addresses. Just now I changed two bytes of the MAC address of my existing router's WAN port. The router took a while, but I did not restart the modem. The router got DHCP of a new outside IP address that differed in 3 bytes. I changed the MAC address back, and I got back my previous IP address. (I have known this for a while. My ISP's DHCP gives each MAC address a 24-hour lease. Changing the MAC gets back the same IP address, unless the lease ran out. Recommendation: Clone your old MAC whenever you change routers, if only to stay at the same IP address. Possible hack: If one or many users change their connected router's MAC every few seconds, eventually the ISP's DNS server will run out of IP addresses. If that happens, it will be "stuck" until the oldest unrenewed leases expire. It could re-issue old IP addresses that have been inactive the longest, but at risk of address collision. Maybe cable-modem DHCP tables include modem addresses, which would let it block collisions caused by forced re-use (and block spoofed traffic too). Maybe cable-modem DHCP limits the number of IP addresses assigned to each modem, voiding the least-recently used one (if needed) when assigning a new one.)
I will update here if an answer arrives.
Meanwhile, a weak "answer" is to insert a non-DD-WRT router, wired-only (or disable the wireless port) between the modem and your DD-WRT router. The non-DD-WRT router will get an IP address from the modem, and the DD-WRT router will get an IP address from the non-DD-WRT router, and all will have Internet access. Two routers, two bottlenecks. And if you need port-forwarding, you have do it twice (once in each router). (By the way, port forwarding or port-range forwarding (I forgot which) severely slowed down one of my routers.) One possible minor benefit is that computers connected to the DD-WRT router can "see" (address) computers connected to the non-DD-WRT router, but computers connected to the non-DD-WRT router cannot "see" computers connected to the DD-WRT router.