What are the limits to lateral Centre of Gravity imbalances?
Lateral c.g. limits are prescribed for large aircraft both for max fuel imbalance and for what is being carried in the fuselage. It's basically impossible to exceed the max lateral imbalance in a passenger aircraft. Exceeding the max in wide body cargo aircraft can be done and is checked for, but it takes an unusual load to exceed the max.

The 747-400, for example, has a max lateral imbalance of 10,000,000 inch-pounds. If you load 207,205 lbs on one side only of the main deck of a 747-400 freighter using size code M pallets, you will exceed the maximum. To see this happen (if you're using Firefox or Chrome--IE won't work) go to 747.terryliittschwager.com, dismiss the flash screen, and then click on test load #6 near the bottom of the page. That will trigger exceeding the lateral imbalance limit. Scroll down to the Lateral Load Imbalance graphic to see the max lateral loading envelope and the point that shows the load exceeding it.

Here are some approximate weights for a 747-400 freighter:

basic operating weight 365,000 lbs

max fuel 360,000 lbs

max cargo 245,000 lbs given the 610,000 max zero fuel limitation and a 365,000 bow

Note that you cannot carry max fuel and max cargo. A common 747-400 max takeoff weight is 875,000 lbs.