But the same LTE modem works fine when connected to ether1?
In theory you should be able to connect either modem/router to either ether1 or ether2 and have the connection, the two interfaces are (should be) exactly the same for all that matters.
Since the LTE modem gives the routes, the DHCP server on it and the DHCP client on the Mikrotik are working.
What do you mean you have no internet?
Like you cannot navigate from your PC or you cannot ping (say) 8.8.8.8 (both from your PC and from the Mikrotik terminal)?
The relevant settings of the two interfaces are seemingly identical, and both are WAN, so the masquerade rule applies to both as well as the (default) firewall rules:
/interface ethernet
set [ find default-name=ether1 ] comment=WAN_ISP poe-out=off
set [ find default-name=ether2 ] comment=WAN_LTE
/interface list
add comment=defconf name=WAN
add comment=defconf name=LAN
/interface list member
add comment=defconf interface=bridge list=LAN
add comment=defconf interface=ether1 list=WAN
add interface=ether2 list=WAN
/ip dhcp-client
add comment=defconf interface=ether1
add comment=LTE interface=ether2
/ip firewall nat
add action=masquerade chain=srcnat comment="defconf: masquerade" \
ipsec-policy=out,none out-interface-list=WAN
Still, there is something that I cannot understand in your report(s).
With both devices connected you had (in Green the ether1, in red the ether2 related routes):
Flags: D - DYNAMIC; A - ACTIVE; c - CONNECT, d - DHCP; + - ECMP
Columns: DST-ADDRESS, GATEWAY, DISTANCE
DST-ADDRESS GATEWAY DISTANCE
DAd+ 0.0.0.0/0 5.187.172.1 1
DAd+ 0.0.0.0/0 192.168.1.1 1
DAc 5.187.172.0/22 ether1 0
DAc 192.168.1.0/24 ether2 0
DAc 192.168.88.0/24 bridge 0
When you have only the ISP modem connected to ether1 you have (correctly):
Flags: D - DYNAMIC; A - ACTIVE; c - CONNECT, d - DHCP; + - ECMP
Columns: DST-ADDRESS, GATEWAY, DISTANCE
DST-ADDRESS GATEWAY DISTANCE
DAd 0.0.0.0/0 5.187.172.1 1
DAc 5.187.172.0/22 ether1 0
DAc 192.168.88.0/24 bridge 0
When you have only the LTE modem on ether2 you should have:
Flags: D - DYNAMIC; A - ACTIVE; c - CONNECT, d - DHCP; + - ECMP
Columns: DST-ADDRESS, GATEWAY, DISTANCE
DST-ADDRESS GATEWAY DISTANCE
DAd 0.0.0.0/0 192.168.1.1 1
DAc 192.168.1.0/24 ether2 0
DAc 192.168.88.0/24 bridge 0
If you can reproduce the first one (with both routers connected and the 4 routes, the 2 green and the 2 red ones) what happens when you disconnect ether1?
The two green routes should disappear, but the two red ones should remain.
And if you remove the LTE from ether2 the two routes should disappear, and return, exactly the same, when you connect the LTE to ether1.