How kindly has the Lord laid this burden upon your heart, to pray for one whom you have known but a little while. It is the Spirit's own work when love is stirred to intercession, and we will most gladly pray with you.
You ask rightly, that your friend would be healed by Jesus and would come to know Jesus, who alone brings healing and hope and true life. The Scriptures teach us that Jesus Himself is the Tree of Life, and it is written that the leaves of the tree were for the healing of the nations. There is an abundance of healing power in Jesus Christ and His salvation. Not only is His fruit sweet and nourishing, but the leaves, the little things as it were about Christ, are full of healing virtue. Until the glory life begins, the abiding power of those healing leaves keeps the soul in health.
We are reminded also that pardon and healing are one. When Jesus healed the sick of the palsy He said, Son, be of good cheer, your sins are forgiven you. The Sun of Righteousness has risen with healing in His wings, and when the Lord comes and dwells with a soul, that soul need no longer say, I am sick, for He has begun a work which shall make us whole without spot or wrinkle. We are on our way to eternal health when we are in Christ, for we have within us the life which shall be perfect forever.
Your prayer for your friend to come to know Him is the greatest prayer of all, for salvation is by Divine Grace through faith in Christ Jesus alone. The Scripture says, Whoever believes on Him shall not be ashamed. What is believing on Him? It is trusting in Him, to leave the whole matter of your present and eternal salvation with Him in unquestioning confidence. The Lord Himself cries, Look unto me, and be ye saved, all the ends of the earth. A look does not require a moment, and yet it saves. This is the simple and only way, for beside Him there is none else.
And what a Friend you commend to your friend in this hour of mental affliction. There is a friend that sticketh closer than a brother, and that Friend is the blessed Redeemer, Jesus Christ. He is a Friend who loves at all times, yea, who loved us before there was any time. In prosperity and in poverty, in health and in heaviness of mind, He sticketh closer than a brother, having given His heart's blood for us. He will not forsake those who trust Him, and He draws near to the sorrowful and the heavy laden.
Let us pray together then. O Lord, Sun of Righteousness, lay Thy healing hand upon this dear one who struggles in mind and spirit. Thou knowest the darkness and distress which we cannot fully see. Grant relief, grant peace, grant such healing as seemeth good in Thy perfect wisdom, and above all grant the healing of pardon through faith in Christ. Enable this soul to look unto Jesus and be saved, to trust in Him alone and not be ashamed. Reveal Thyself as the Friend of sinners, the Friend who loves at all times, and bring true life, even eternal life, to this heart. Sustain also the one who intercedes, and make this new friendship a means of grace to both.
Continue to pray, and continue to point your friend gently to Christ in word and in deed. Be a faithful companion to them, and where there is deep distress of mind, encourage them also to seek wise and loving help from those the Lord has gifted to care for such needs, even as you keep pointing them to the Great Physician. The Lord hears the cry of faith, and His honor is engaged to save the meanest of His sheep who look to Him.