/interface detect internet is not part of the firewall, it is something that very few people actually use, let alone need, and is known to mess things in some subtle ways in some configurations.
Disabling it is usually advised, see:
http://forum.mikrotik.com/t/what-is-detect-internet-for/159604/1
In the best cases it does nothing useful, in the worst it may mess with DHCP (which seems like your case, though it has to be tested if it is actually connected to your issue).
Summing it up, your report says:
DSL works on ether1 but not on ether2.
LTE works on BOTH ether1 and ether2.
This makes me think that the issue is related to something in the DSL modem/router that is somehow providing the IP address via DHCP to ether1 but not to ether2, (which is what comes out from your /ip route print outputs posted)
Maybe you need to reboot the DSL router after having moved the DSL connection from ether1 to ether2?
The fact that the LTE works indifferently on ether1 and ether2 is a confirmation that (on Mikrotik’s side) the two ports are set exactly in the same manner (good).
In any case, you can keep the DSL on ether1 (working) and the LTE on ether2 (working).