The lines "Now lap-dogs give themselves the rousing shake, / And sleepless lovers, just as twelve, awake" appear in the third stanza of canto 1 of Alexander Pope's mock epic The Rape of the Lock. The poem, which focus on the "tragedy" of the coquette Belinda, whose suitor steals a lock of her hair, is designed as a satire of upper-class life and its silly, shallow routines, scandals, and relationships.
The lines in question enter directly into that satire. The day is just beginning for these frivolous people. As the sun peaks through the curtains, little lap-dogs shake themselves awake. They have been curled up asleep with their masters and mistresses, "guarding" them from danger, though these "fierce" little beasts could only nip at the ankles of an intruder (if the lazy creatures would even do that).
The dogs are not the only ones rising to greet the new day. Of course, half of that day has already passed, for it is already noon. The "sleepless lovers" are finally waking up. Notice the paradox here. These lovers are supposed to be too lovesick to sleep. They are supposed to be staying up all night, scheming and planning how they will win their beloved or grieving a lost love. Yet it is noon, and they are just opening their eyes. They have not lost any sleep for love that night (or morning), and perhaps their love isn't all that strong in any case.
Notice Pope's sharp satire here. The characters in his poem are lazy at best, sleeping half the day away and then rising as if it were early morning. Their emotions seem to be shallow and weak, yet as the poem continues, they will find the highest of drama in the smallest of incidents.