First off let me say that THIS IS JUST MY OPINION as to how I thought "Dawn of Justice" would have made more sense.... With that said I'm disappointed in the decision to introduce doomsday so early and with such a poor origin that throws the movie and upcoming sequels off track.
Well for starters instead of lex experimenting with Zod's body and creating Doomsday he created Bizarro instead??
His motive to kill superman and anyone who stands in his way would be stronger and way more practical!! However also during the movie he could pose as superman's doppleganger and frame him for many atrocities which would justify batman wanting to bring superman aka the "false god" to justice. The militia we saw would have been government appointed but funded by lex and have bizarro lead them on many onslaughts over the world.
At one point batman goes after superman but supes is aware of bizarro and he has to convince batman that he is being framed. Wonder Woman becomes suspicious of lex luthor, she learns about his dark endeavour and threatens to expose his diabolical plan to kill superman, become the President of America and take over the world with bizarro and his army. Lex sends Bizarro to attack wonder woman and during the fight batman and superman show up.
This is when Lex shows up in his mech suit and kicks superman's butt all over the place, Luthor unveils a "mother box" which is a tech used by Darkseid to travel throughout dimensions. At one point lex opens a boom tube to Apokalips in an attempt to suck superman in but instead batman and wonderwoman manage to knock bizarro into the portal. As the wormhole is becoming larger swarms of parademons fly out and lex flies off leaving Batman, Superman, Wonder Woman, Cyborg and Flash to fight off the invasion. Superman regains his strength and tears through the parademons, batman instructs flash to find Luthor and retrieve the mother box. Bizarro flies back through the boom tube and takes out a few of the parademons before he shot down by an omega beam, all the heroes see a dark figure climbing out of the portal and they do their best to focus their attacks on him but he is indestructible.
Aqua man shows up and tries to drown Darkseid but he can stop him, Flash convinces Luthor to give up the mother box and returns as they all make one desperate attempt to stop Darkseid. Aquaman causes the ocean to rise over Darkseid as flash runs around him so fast that it creates a vortex encapsulating the being in water, superman uses his cold breath and a weakened Bizarro uses his ice vision to quickly freeze Darkseid in an iceberg like tomb, Aquaman, Superman, Bizarro, even Lex Luthor use their might to push Darkseid back through the boom tube and flash activates the mother box which closes the portal. Cyborg, Batman and Wonder Woman dispose of the remaining parademons, Bizarro dies because without a red son his body couldn't heal but he went down as a hero. Months after the incident Lex Luthor is running for president and vows to protect the world from alien invasions, he offers a truce to superman and the other heroes publicly and inaugurates the Justice League as the protector of Earth.
After all this Lex Luthor did not only get his hands on Zod's body, he also got Nam-Ek's (He wasn't sucked in the phantom zone in MoS) corpse locked away in a deep underground lab! As a sequel for Man of Steel 2 Lex Luthor tries recreate his experiment with Zod on Nam-Ek's body but because Nam-Ek's body was mutated with the serum of a wild Kryptonian beast he ended up creating Doomsday!!!
Who is Nam-Ek? here's a brief background on him