Lancer was specifically ordered to scout out the other masters and determine their Servants' strengths by fighting them to a draw. He couldn't expect to get a proper measure of Saber or Archer's strength, who were going to some lengths to hide their abilities—indeed, both Saber and Archer were going on about how their "true" weapon could be anything, but they weren't going to bother revealing it—, unless he tried to force their hands. In a battle between Servants, this pretty much always requires the use of their most powerful Noble Phantasms. While use of his Noble Phantasm could result in the deaths of either Saber or Archer, it seems likely that either the Command limited the potency of the attack, or that the vagueness of "find out their strengths" allowed him a bit of a loophole against such secretive opponents. A Command not to kill them would seem likely to interfere with a Noble Phantasm to some extent, perhaps giving the opponent just enough wiggle room to avoid death (but not necessarily a severe injury, such as with Saber).
According to the TypeMoon wikia:
Contrary to his legendary battle prowess, his fighting in the Fifth Holy Grail War is extremely limited. Fighting several Servants to a draw, he will never start a fight on his own. Even if he gains a full chance to kill an opponent, he is to merely observe and is given no authority to attack. He can only go all out against an opponent during their second encounter due to the Command Spell, so his first true "battle without any binds" is against Archer. Without anything binding him, his strikes are much faster and harder to see than in the previous battle. The only way Archer is able to keep up with him in direct combat compared to the previous fight is due to the experience of previously fighting him.
Recall that Lancer was initially attacking Shirou before Saber had been summoned. Shirou was simply an outside witness, and by Rin's commentary this was strictly disallowed, and so it was completely natural that Servants would disengage from their own fights to eliminate the witness. Once Saber is summoned, Lancer backs off and waits for Saber to come to him and force the combat (thought he doesn't seem to have problems with trying to provoke his opponents). For the preceding fight with Archer, we do not know exactly how it was initiated. We are introduced to the fight already in progress from Shirou's perspective.
