Correct me if I'm wrong, but during the 18th and early to mid 19th centuries, the Company was typically the smallest unit to be given independent orders, ie "Corps commander passes orders down to his Division Commanders, Division Commander to his Regimental Commanders, Regimental Commanders to their Company Commanders who shepherd their men to perform the movement."
Since Company commanders tended to be Captains, what role did Lieutenants play in these operations? In modern war, Lieutenants are almost always given a fair amount of independent decision making, especially in recent American operations in Iraq and Afghanistan. I am unsure of how current command delegation compares to Napoleonic styles.
Ethymologically, lieutenant comes from the French and meant "place-holder". He was therefore to "hold the place" of the captain whenever the Captain was not there, whether because he had other obligations, was wounded, dead etc...
Also if a group had somehow to be separated for the rest of the company such as to escort a convoy the Lieutenant would be given command of the group.
This last role evolved as the one we have today with the Lieutenant assuming command of each individual platoon and the captain commanding the company as a whole.
Generally, it's incorrect to say that a company was the smallest unit to be given independent orders, at least in the French army.
A French battalion was made up of six to eight companies, depending on the time period; made up of a company of Grenadiers, four to six companies of line infantry, and then one company of voltigeurs (skirmishers). Each company had different purposes and thus could only work effectively as a battalion.
So from this, it must be said that Captains, at least French Captains, didn't have very much in terms of independent orders since the battalion was the smallest independent unit. A Major would command a battalion and basically be given orders from either his regimental commander or the brigade commander (depending if it is an independent battalion or a part of a regiment) and fight as told.
When a battalion was deployed in line the lieutenants were stationed directly behind the company with 2 sergeants and a sergeant-major. LTs job was to make sure no man ran, act as a second set of eyes for the Captain, and take his place if necessary.
Captains and LTs in light infantry companies had the greatest opportunities to really command their troops. When in skirmish order a company of 80-100 men was too spread out to be commanded by one person. This is where the LTs would be of use. This is an example of a French company in skirmish order taken from http://www.napolun.com/mirror/napoleonistyka.atspace.com/infantry_tactics_4.htm