That is not Biblical. Nowhere can you find said caveat in the promises of Jesus regarding faith and answered prayers. Nowhere did He add "if it's in God's will" at the end of His promises. The fact that The Lord's Prayer contains the statement "Thy will be done" does not invalidate the numerous Biblical promises that all the prayers said with faith will be granted.
Then you're not taking the full teaching on prayer as given in Scripture. Jesus says more than that and the NT as a whole says more than that. That prayer is to be according to God's will should go without saying. God isn't going to give everything asked in prayer just because it was asked. He isn't a genie.
Luk 22:41 And he withdrew from them about a stone's throw,
and knelt down and prayed,
Luk 22:42 saying, “Father, if you are willing, remove this cup from me.
Nevertheless, not my will, but yours, be done.”
Luk 22:43 And there appeared to him an angel from heaven, strengthening him.
Luk 22:44 And
being in agony he prayed more earnestly; and his sweat became like great drops of blood falling down to the ground. (ESV)
Joh 14:13 Whatever you ask in my name, this I will do, that the Father may be glorified in the Son.
Joh 14:14 If you ask me anything in my name, I will do it.
Joh 14:15 “
If you love me, you will keep my commandments.
Joh 14:16
And I will ask the Father, and he will give you another Helper, to be with you forever,
Joh 14:17 even the Spirit of truth, whom the world cannot receive, because it neither sees him nor knows him. You know him, for he dwells with you and will be in you. (ESV)
Joh 15:7
If you abide in me, and my words abide in you, ask whatever you wish, and it will be done for you. (ESV)
Act 12:5 So Peter was kept in prison, but
earnest prayer for him was made
to God by the church. (ESV)
Rom 8:26 Likewise the Spirit helps us in our weakness.
For we do not know what to pray for as we ought, but the Spirit himself intercedes for us with groanings too deep for words.
Rom 8:27 And he who searches hearts knows what is the mind of the Spirit, because
the Spirit intercedes for the saints according to the will of God. (ESV)
Rom 15:30 I appeal to you, brothers, by our Lord Jesus Christ and by the love of the Spirit,
to strive together with me in your prayers to God on my behalf, (ESV)
Eph 6:17 and take the helmet of salvation, and the sword of the Spirit, which is the word of God,
Eph 6:18
praying at all times in the Spirit, with all prayer and supplication. To that end, keep alert with all perseverance, making supplication for all the saints, (ESV)
Jas 4:2 You desire and do not have, so you murder. You covet and cannot obtain, so you fight and quarrel.
You do not have, because you do not ask.
Jas 4:3
You ask and do not receive, because you ask wrongly, to spend it on your passions. (ESV)
Jas 5:14 Is anyone among you sick? Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord.
Jas 5:15 And
the prayer of faith will save the one who is sick, and the Lord will raise him up. And if he has committed sins, he will be forgiven.
Jas 5:16
Therefore, confess your sins to one another and pray for one another, that you may be healed. The prayer of a righteous person has great power as it is working. (ESV)
1Jn 3:21 Beloved,
if our heart does not condemn us, we have confidence before God;
1Jn 3:22 and whatever we ask we receive from him,
because we keep his commandments and do what pleases him. (ESV)
And on it goes. There are conditions to prayer being answered. As I stated earlier, if God isn't giving you what you're asking for in prayer, then likely something is wrong--with what you're asking for, how you're asking for it, your spiritual life, lack of true faith, etc. However, it could be that God wants you to persevere in prayer. Some people pray for the same thing for decades before seeing a prayer answered.
I strongly suggest, if you haven't done so, to read some books on prayer, such as Prayer: The Cry for the Kingdom, by Stanley Grenz and The Power of Prayer and the Prayer of Power, by R. A. Torrey.
God can do anything, including tell lies, and He will make it clear to you that it's a lie. To lie is not always the same as to deceive. You can tell a lie to someone after you've informed them that you will be telling them a lie. God could simply grand said prayer by stating: I will tell a lie to you: all grass is blue. That was the lie.
Why would anyone tell a "lie" by prefacing it by saying they're going to tell them it's a lie? What purpose would that serve? A lie is, by definition, either something intended to mislead or deceive, or it something that is false or inaccurate but may be believed to be true by the speaker. Otherwise it serves no purpose. So, no, God cannot do anything, including lie.