All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
May Allaah reward you well for your keenness on inviting your family to good and teaching them about Islam. Calling people to Allaah The Almighty is one of the best deeds that the Muslim individual can do. Allaah The Almighty says (what means): {And who is better in speech than one who invites to Allaah and does righteousness and says, "Indeed, I am of the Muslims."}[Quran 41:33]
Ibn Katheer reported in his Tafseer (interpretation of the Quran) that Al-Hasan Al-Basri said regarding that verse: "This is the close friend of Allaah, this is the beloved of Allaah, this is the chosen one among Allaah's slaves, he called people to Allaah The Almighty and responded to the call of Allaah."
Amongst the basic principles of calling people to Allaah is choosing the appropriate time and condition when one thinks that they would likely accept his call. It was narrated that ‘Abdullaah ibn Mas‘ood said: "The Prophet, sallallaahu ‘alayhi wa sallam, would take care of us in preaching by selecting a suitable time, so that we might not get bored." [Al-Bukhari and Muslim]
Also, the caller should deal with the laymen whom he calls to Allaah among those who neglect the orders of Allaah The Almighty according to their conditions, i.e. that they could be ignorant and negligent and need a kind of softening their hearts. He should not deal with them as if they were like him in acquiring religious knowledge and responding to Allaah's commands. Allaah The Almighty says (what means): {You [yourselves] were like that before; then Allaah conferred His favor upon you, so investigate. Indeed Allaah is ever, with what you do, Acquainted.}[Quran 4:94]. Unfortunately, many of the callers to Allaah may neglect that matter.
Accordingly, talking with your family regarding some lawful matters may be a reason of winning their hearts and having greater effect on them. So, do not stop doing it; rather, make it a means of calling them to Allaah The Almighty. However, if it is about something evil such as backbiting and the like, then you should not go along with them in it. But, you have to adopt a kind approach to get them away from it. For more benefit about the best means of calling people to Allaah The Almighty, kindly refer to Fataawa 16844 and 87573.
As for the explicit lying, it is not permissible at all unless it is necessary to save the Muslim individual from a critical situation. Actually, Islam has granted us a great alternative to lying which is using equivocations (Tawriyah, i.e. saying something which has more than one meaning and intending a meaning different from what the listener is likely to understand). For more details, please refer to Fataawa 84728 and 88412.
Allaah Knows best.