No, Friar Lawrence was not kept in quarantine; it was Friar John, the person responsible for delivering Friar Lawrence’s letter, who was forced to quarantine when it was suspected that he had been in close contact with sick people. This letter is important because it details the plan for Juliet to fake her own death with Friar Lawrence’s potion, and it explains what Romeo should do in order to retrieve her, very much alive, from her family’s mausoleum. When Friar John explains that he was detained in quarantine and returns the original letter to Friar Lawrence, Friar Lawrence immediately begins to fear that the plan will go awry.
For now, Friar Lawrence fears that Juliet will awaken in her crypt all alone, no Romeo by her side, and that she will be scared and upset. He plans to retrieve her himself, asking Friar John to bring him a crowbar so that he can force the gates of the mausoleum open, and then he will hide her in his own cell until he can get Romeo to come. He does not seem to suspect that Romeo will hear, in some other way, that Juliet is dead and that this news might cause Romeo do to something drastic.