I'm not a scholar, but I'm referencing scholarly sources and my own research.
First of all, the issue of growing organs in a lab is so new that I haven't been able to find much on that specific topic. That said, it is analogous to the issue of cloning. I've found a very comprehensive answer, but here's the summary:
"Cloning is simply reproducing one or more living being(s), either by transforming the nucleus from a body cell into an ovum whose nucleus is eliminated, or by dividing a fertilized ovum at a stage that precedes the acquisition of distinct tissues and organs.
It is no secret that such procedures and processes are not a creation or some of the creation process, for Almighty Allah says:
1- (Say: who is the Lord and Sustainer of the heavens and the earth? say: (it is) God. say: do ye then take (for worship) protectors other than him, such as have no power either for good or for harm to themselves? say: are the blind equal with those who see? or the depths of darkness equal with light? or do they assign to God partners who have created (anything) as he has created, so that the creation seemed to them similar? say: God is the creator of all things: he is the one, the supreme and irresistible) (Ar-Ra`d13: 16)."
Related to this is the issue of stem cell research, which you may also find interesting. (http://www.onislam.net/english/ask-the-scholar/health-and-science/genetics/175298.html)
It's also important to understand how organs are grown. From my research, I've found that organ "growing" is a bit of a misnomer. It's not as though scientists just take a bunch of empty matter and turn it into a lung or a heart. What most often happens is that an existing donated organ, lets say a heart, is essentially stripped of its existing cells leaving an empty collagen structure behind. This is called a "scaffold".
This is where stem cells come in. Stem cells are like the building blocks, in that they can be, in essence, "trained" to act in a specific way (see the above source on stem cells for a more detailed explanation.) Stem cells are taken from a patient's body and introduced into the scaffold, which then "grows" new cells, and is then transplanted into the patient's body. The Islamic ethics on this are still up for debate, of course. But there are a few important points to keep in mind: 1) medical science uses pre-existing material to do this. It's not like science is creating something out of nothing. Even in the case of using a 3D printer to "print" an organ, the printer still requires a) proper cellular material, and b) the proper schematic for the organ. The printer is incapable of doing these things on its own. 2) Historically, Islam has been very open towards scientific discovery. We live in an age of science and innovation, and such things must be viewed through the lens of our faith to understand it. Science can explain "how" a thing happens, but not the "why". 3) There is still a limit to what science can actually do. For instance, attempts to grow a full brain, liver, kidney, and eye have not been successful. These structures are so complex and perfectly formed, as is, that even the most advanced scientific techniques cannot imitate them. That just shows how everything was created with a specific form and function, laid out by God. As for imitating the creation of God, perhaps this has to deal more with the intention of the person growing the organ. For argument's sake, let's say it was a Muslim scientist, who was operating under the full knowledge that he or she was simply taking what God had already created and working with it to create something beneficial, and was not tempted to think that made them a creator or partner with God.
I'm not sure if this answers your question, but I do hope that it helps you feel a bit more sound in your faith.