No - your order would be "The 7/21 Lancers shall charge the 2eme Regt de Ligne" and when they form square, your Lancers do not have orders to charge another unit. Your best bet is to break the infantry, meaning they cannot form square, and then put them out of their misery with the Lancers.
Hope this helps!
There can be no doubt that the success of the attack on and stand against the enemy at St. Lambert sur Dives can largely be attributed to this officer’s coolness ... London Gazette, no.36812, 27 November 1944
The rule for squares on pages 74/75 do not say whether you can or can't charge another enemy, only that the cavalry move to a point 3 inches away from the square and then use up the rest of their movement either going back from where they started or around the square.
Grant's answer is correct if you have used an order similar to the one he has used as an example. However, if you just gave a general "Charge" order without specifying an enemy unit, then I suppose that you could do as you have suggested, as long as the next enemy unit met all of the conditions at the start of the cavalry unit's move. In other words, the cavalry must have line of sight to the enemy unit when it starts it's charge move.
Hmm, Wellington's cavalry in attack would charge everything in sight. Getting out of control. Attacking until being destroyed or scattered by the better led French cavalry. The Union Brigade charge at Waterloo is only the best known of a long list of these fox hunter attacks.
If a cavalry unit is given an order to charge the enemy infantry and gets three moves, Should it not be able to charge towards and around a newly formed square and then on to any other exposed infantry.