Not if you only have the Sentinel feat
The Sentinel feat (PHB, p. 169-170) is specific on when it engages:
Creatures provoke opportunity attacks from you even if they take the Disengage action before leaving your reach.
When a creature within 5 feet of you makes an attack against a target other than you (and that target doesn't have this feat), you can use your reaction to make a melee weapon attack against the attacking creature.
In the case you provide of a creature entering your reach, neither of those qualifiers are met. The creature isn't leaving your reach, it is only just entering and the creature isn't in 5' of you and hasn't attacked an ally. Therefore you don't get an opportunity attack upon the creature entering your reach.
The Polearm Master feat does synergize with this, but not with a Lance
The Polearm Master feat (PHB, p. 168) says:
While you are wielding a glaive, halberd, pike, quarterstaff, or spear, other creatures provoke an opportunity attack from you when they enter your reach.
This is the feat/clause that let's you take an OA when a creature enters your reach. Without it, you can't do it :(
But there can be only one
It is important to remember that you only get one reaction that refreshes at the start of your next turn.
When you take a reaction, you can't take another one until the start of your next turn. If the reaction interrupts another creature's turn, that creature can continue its turn right after the reaction.
This means that you can either use that reaction and take an opportunity attack when a creature enters your reach (via Polearm Master) or use it when leave your reach (via Sentinel). You can't use both, so you'll have to decide if it is better to take it when the creature is coming or going.