You're not really looking for the C rating (maximum discharge current in multiples of nominal capacity), you're looking for the adjusted capacity at your nominated discharge current.
A 1.8Ah lithium battery can theoretically give 1.8A for 1hour, or 3A for 1.8/3h = 36 minutes. HOWEVER the capacity for a battery is traditionally quoted for a 20 hour discharge. That is, a capacity rating of 1.8Ah means the battery delivered 90mA for 20 hours in testing.
The relationship between continuous current and time-to-full-discharge is NOT linear. You have discovered that when discharged at 3A, your 1.8Ah battery is delivering much less capacity (only about a quarter!) than a linear interpolation of the amp-hour rating would suggest. This is not unusual.
The better batteries will give rated capacity at several discharge time samples, or even a graph of current vs capacity. A battery intended for remote control uses will probably give better performance, as quick discharge is the intended application of these batteries.
(I use a 1500mAh 3-cell (11.1v) 25C lithium pack to power a 3A LED bike light, and I get around an hour, which is close to rated capacity given a reasonably efficient buck regulator).
How do you determine how many cells are in a Lithium battery?
My assumption is for customer travel and the present limits are;
• MAX Lithium per cell 20Wh
• MAX Lithium per battery 100Wh
The battery in question.

LP635940 Lithium Polymer Battery
3.7V @ 1.8Ah typ. capacity at 0.2C rate
= 6.66 Wh which is less than MAX per cell limit.
How many cells in package?
Only 1.
Not because of capacity but because of construction method.
What are cells?
- discrete (separate) manufactured items.
How many items here?
1
How is it made?
Many recurring thin layers of {conductor mesh , electrolyte, insulator}.
Best Answer
A cell of 1Ah releases a charge of 3600 Coulombs, or 0.0373 mol. Since one nickel atom is required to produce 1 electron in Ni-MH chemistry, a cell of 1Ah needs a least 0.0373 mol of Ni, which is 2,19 grams of pure metal, assuming 100% of Ni(OH) participates in the reaction.
So, Ni-MH batteries contain at least 0,219 kg/100Ah of nickel.
And yes, you should have asked it at Chemistry.SE.