lapdog(n = noun.animal) - a dog small and tame enough to be held in the lap;
is a kind of canis familiaris, dog, domestic dog

1.  A small dog which is or can be fondled in the lap. [1913 Webster]

2.  One who does the bidding of another; a servile follower. [PJC]

N  servility, slavery, obsequiousness, subserviency, abasement, prostration, prosternation, genuflection, fawning, tuft- hunting, timeserving, flunkeyism, sycophancy, humility, sycophant, parasite, toad, toady, toad-eater, tufthunter, snob, flunky, flunkey, yes-man, lapdog, spaniel, lickspittle, smell-feast, Graeculus esuriens, hanger on, cavaliere servente, led captain, carpet knight, timeserver, fortune hunter, Vicar of Bray, Sir- Pertinax, Max Sycophant, pickthank, flatterer, doer of dirty work, ame damnee, tool, reptile, slave, courtier, beat, dead beat, doughface, heeler, homme de cour, sponger, sucker, tagtail, truckler, servile, obsequious, supple, supple as a glove, soapy, oily, pliant, cringing, abased, dough-faced, fawning, slavish, groveling, sniveling, mealy-mouthed, beggarly, sycophantic, parasitical, abject, prostrate, down on ones marrowbones, base, mean, sneaking, crouching, hat in hand, cap in hand.