Well, if Ph(OH)2 is soluble in water to any measurable degree (refer to solubility constant) then the Pb2+ ions will definitely be dissociated from the OH- ions. And if you add H+ ions from a dilute hydrochloric acid solution, you're increasing H+ in a solution which ALREADY has elevated OH- content
And remember that Kw = [H+][OH-] = 10-14...the product of those two concentrations can't exceed that number. The concentration in your case HAVE to decrease somehow...and the acid/base reaction you suggested is an ideal way to do that.