@pgr
No, the Lee breakout didn't work, or more correct, it didn't work without giving me Richmond.
As I said earlier, I threw the armies together. Lee attacked and won despite his heavy losses, 7500 vs 3000 casualties.
My stack retreated to the nearby region. The previous turn, a corps was just next to Richmond and I had ordered it to Richmond.
So after that loss, there was again a stack in Richmond.
Lee didn't attack it, my army was there the next turn again, and the final battle was lost by Lee, who then withdrew South.
@tripax
Interesting analysis. I like that!
For my concern for the command penalty, I wanted to optimize my forces to have the greatest chance of capturing Richmond in a few turns.
I had expected the CSA to retreat all troops to defend Richmond, leaving me the valley and able to concentrate my troops South.
However PGT Beauregard threatened Strasburg and J. E. Johnston had his eyes on Harpersferry.
I knew if they joined the defence of Richmond, my attack would fail. Because 2 big stacks of them stayed behind, I took the initiative and attacked Richmond.
I had Butler commanding an army in Suffolk and Franklin leading a corps in Norfolk.
As for the numbers, I know the troops aren't enough to hold Lee inside, but a force of 35.000 leaving a besieged city
with that many guns pointed towards them, is going to suffer more casualties. There probably are only a couple of viable
routes where troops can quickly leave a besieged city. There might be other routes, but these might actually delay an exit and thus
increase the exposure to enemy fire and lead to more casualties.
I do think it's historical that Lee could storm out, leaving Richmond for the taking, but the number of casualties should
have been higher due to the massive gun buildup. Instead he first tried to attack the besieging troops.
It didn't go that way because the engine apparently picks 1 unit to attack to break the siege.
Now depending on how fast such an exit is (can't be super fast if using roads, and even slower if they exit in another way), and how many good escape routes there really are,
not all guns might be used to attack Lee's forces, as from your analysis, the scale is quite vast.
To conclude: escape possible vs 55.000 besieging troops? Yes.
Total casualties: not enough, should be a severe penalty due to the number of total guns and the speed of the exit. Remember he has to exit his 80 guns too.
Or make a quick march out possible but with more material captured or more guns destroyed in doing so as they would probably destroy their own guns.
Victory: first exit was marked as a victory yet Lee stayed in Richmond so he merely attacked and didn't try to exit. He almost lifted the siege but didn't so I wouldn't have called it a victory for Lee.
However, he should get credit as he drove off the stack he attacked, and in a way, that's a victory.
Here are some screenshots.
This one is where Lee exited Richmond instead of just trying to repel the attackers.
The army under McDowell retreated. The corps under Hooker moved back in after being driven of after Lee's first succesful attack and Milroy was also present.
Mind the setup of the armies/corps changed with the start of the siege.

After I took Richmond, the 2 big stacks near Harpersferry started moving South.
As Richmond was under siege, and I had 3 stacks to defend the area, I believe it was a mistake on part of Athena to leave the troops there.
In the end, both stacks got short of supply and they dwindled to a stacks of 250 power, in a big part due to lost cohesion.

Richmond area:

After I took Richmond, I layed siege to Nashville and took it the turn after. Game over by September 1862.
It had been a while since I played the Union but it's far easier compared to the South.
You can optimize armies, get gatlin guns, can afford all the special support units for your armies, get sharpshooters and marines in.
Wow, it's very fun playing as the Union compared to the South.
I didn't set Athena to play very aggressive, yet I felt she sent to many small units on their way to invade.
Once the Union steamroller gets going, you pick off all those small targets and quickly build up victories and morale.
If Athena detects to many troops, she should retreat to strong positions, which she doesn't do.