Answer: It's complicated!
Why? Because when a Narcissist meets you initially and they start the 'love bombing' stage, they are in love with an idealized version of you... a version that has nothing to do with who you really are as a person.
They mirror you and this creates an enigmatic rapport that has you falling head-over-heels before you know what's hit you. But after a while (usually quite short), they start seeing you as a real person who can't live up to their impossibly high, and totally false, ideals of who you should be. So then they start the ‘Devaluing’ stage, and this is where they get really mean, and you’re left reeling from shock because you can’t understand this Jekyll and Hyde behavior they’re suddenly displaying. One minute they adored you, the next, they’re criticizing you, flirting in front of you, withholding sex and affection, and leaving you feeling wretched.
But then again, in a heartbeat, they tell you they love you. Do they? What the hell is going on?
Now back to the question... yes, they are lying. In the beginning they are lying to themselves, because they know the form... you're not the first person they've love-bombed, and you won't be the last. During your relationship, they will almost certainly be carrying on relationships with other sources of 'supply', because one is never enough to satiate their utterly insatiable appetite for Narcissistic Supply.
They are lying because a Narc is truly incapable of real love. A Narcissist is an empty, hollow vessel who needs constant attention, adoration and incessant validation. They exhaust you, emotionally and often physically. They lie, cheat, belittle, degrade and steal - not just your possessions and money, but they aim to seal your self-worth, your life, your very soul.
The use the word ‘love’ as a means to trap you, and to keep you trapped in their web of lies and deceit. The simplest way to gauge if someone really loves you is to judge them by both their actions and their words.
Are they kind, gentle, loving, generous to you? Do they do what they say they’ll do? Do they make promises they keep? Do they love to see you happy and fulfilled? Are they supportive? Do they encourage you to do well, to go out and enjoy time with your friends, to spend time with your family?
Or can you honestly answer NO to all those questions? Do they utterly confuse you with gaslighting, saying one thing and then denying it, spying on you, running ‘word salad’ rings around you and telling you that you are needy, insecure, jealous, suspicious, and accusing you constantly of doing all the things they are doing?
Have they tried to isolate you from your family and friends? Do they constantly talk about themself, and have little time to hear or listen to anything you have to say?
Does this sound like the behaviour of someone who loves you? Ask yourself what love really is, and what it means to you? How do you show your love? What matters most in showing love to you? Are you getting back even a fraction of what you’re putting into the relationship?
If you are living with a Narcissist, then you are not loved. You’re being used, abused, and you will be destroyed and discarded. It’s only a matter of time. My advice is and always to get out of the relationship and start living your life in freedom again.