It all really depends on how you're going to operate.
You can figure out how many amp hours you'll need like this...
As an example, let's say on average you're going to transmit for 10 minutes out of every hour.
So for those 10 minutes, you're going to draw 23 amps for 100 watts output.
And for the rest of the time, you'll be receiving. So 50 minutes at a current draw of about 1 amp.
10 minutes is 1/6 of an hour, and 50 minutes is 5/6 of an hour. So for each hour, your current consumption will be:
((1/6) * 23) + ((5/6) * 1) =
3.83 + 0.83 =
4.66 Amp Hours of battery capacity for 1 hour of operation.
And you can continue doing that until the battery voltage drops to the lowest voltage your radio needs to work properly.
Most rigs require 13.8V +/- 15%. So once the voltage on the battery drops to 11.7V, then you're done, and need to recharge.
Knowing that, you can now select what kind of battery to use.
For the Lithium chemistries, it's safe to go to an 80% depth of discharge (DOD).
For lead-acid chemistries, is safe to go to a 50% DOD. Why do you have to consider DOD?
Because you can NEVER use all the energy stored in a battery without seriously reducing the number of usable charge/discharge cycles you'll get out of it.
Now divide your required amp hours by the DOD to figure how much capacity you really need per hour.
You mentioned Lithium, so 4.6 / 0.8 = 5.7 Amp Hours of capacity for each hour of operation, assuming the 1:6 ratio of transmitting to receiving illustrated above. If you transmit more, you'll need more, if you transmit less, you'll need less.
Want to make your battery last longer? Then reduce your transmitter power. 50W is still a very effective power level for operating CW. When I operate CW portable, like for Field Day, I usually only run 20 watts output.
How many hours do you want to be able to operate at a time? Let's say you want to be able to go for 4 hours.
Then you'd need 4 * 5.7 = 22.8 Amp Hours of battery capacity with a Lithium chemistry to operate for 4 hours.
Want to go for 8 hours? Then you need 8 * 5.7 = 45.6 Amp Hours of capacity.
Hopefully you find this helpful. And I hope you have loads of fun operating battery powered portable!
73 de N8AUC
Eric