You not ask about that in your Question Post#1 but for inspiration please read, analyze, apply this one:
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Bandwidth-based load-balancing with failover. This presentation also covers Mangle.
This was presented at the MUM (MikroTik User Meeting) in New Orelans, USA.
Tomas Kirnak - YouTube: > https://www.youtube.com/watch?v=67Dna_ffCvc&t=1s
http://mum.mikrotik.com/presentations/US12/tomas.pdf
This is very good way to setup “MultiWAN” but it’s very very good to learn about traffic on multi interface’s. For me it’s next step for you to do.
Even if your LTE haven’t a PublicIP and you not receive traffic from LTE even do still the way of setup cover many aspects.
The way to send traffic to internet can by done by Route>Rules; Firewall>Mangle rule via script’s…; PCC; hand change; Route Distance… even this is just way to send traffic into web and upper material give more.
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But I still do not have any internet connectivity. Any help you can provide would be appreciated!
I miss read this part. I will import your setup and edit this post. Please wait. I still your project and I must add tho VM as client-s of both your LANs.
See this:

About your config, this part is bad:
/ip dhcp-client
add dhcp-options=clientid,hostname disabled=no interface=ether1-lte use-peer-dns=no
add dhcp-options=clientid,hostname disabled=no interface=ether2-dsl use-peer-dns=no
Means both have distans default=1 and no one is Active, you should on one of them add this:
default-route-distance=2
means:
/ip dhcp-client
add default-route-distance=2 dhcp-options=hostname,clientid disabled=no interface=ether1-lte
add dhcp-options=hostname,clientid disabled=no interface=ether2-dsl
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You configure DHCP Server by hand, not from WinBox? I not see the dhcp network entry.
DHCP-Server Wizzard work from CLI too: /ip dhcp-server setup
/ip dhcp-server network> add address=10.0.1.0/24 gateway=10.0.1.1 dns-server=1.1.1.1
/ip dhcp-server network> add address=10.0.3.0/24 gateway=10.0.3.1 dns-server=1.1.1.1
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Next, you have PC behind your Router, you need NAT, means SNAT to hide your PC in internet and share internet to them.
/ip firewall nat add out-interface-list=WAN chain=srcnat action=masquerade
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After this correction of your setup my GNS3 VPCS’s have access to internet and one by LTE and second one by DSL - checked by tracert.
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Finally was able to get a test lab setup at home where I could work on this configuration.
I recommend you to install GNS3 VM via my HowTo:
https://gns3.com/community/discussion/gns3-with-workstation-player-15- → By Marcin Przysowa OCTOBER 19TH, 2019
On All MikroTik in GNS3 I can logon via WinBox by using RoMON - very helpful.
I hope I help you with your setup.
Good Luck.