Give Metropolis Reformer indestructible, and then deal damage to Metropolis Reformer.
Metropolis Reformer and Blazing Sunsteel trigger.
Resolve the Metropolis Reformer trigger, causing you to gain life equal to the damage dealt.
Resolve the Blazing Sunsteel trigger, dealing that much damage to Metropolis Reformer.
Repeat from step 2.

Infinite damage

Infinite lifegain

Infinite lifegain triggers

Blazing Sunsteel

Metropolis Reformer

Cast Angel's Grace by paying {W}, causing all damage that would reduce your life total to less than one this turn to reduce your life total to one instead.
Cast Volcano Hellion by paying {2}{R}{R}.
When Volcano Hellion enters the battlefield, it triggers, dealing an arbitrarily large amount of damage to you and Metropolis Reformer, with your life total instead becoming one due to Angel's Grace.
Metropolis Reformer triggers, causing you to gain life equal to the damage dealt to it.

Volcano Hellion

Angel's Grace

Cast Volcano Hellion by paying {2}{R}{R}.
When Volcano Hellion enters the battlefield, it triggers, dealing an arbitrarily large amount of damage to you and Metropolis Reformer.
Metropolis Reformer triggers, causing you to gain life equal to the damage dealt to it.

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