Why was the lifter so out of control?

The deployment of the crane is what destabilizes it.

When the Xeno got on board the lifter, Daniels order Tennessee to unlock the robotic arm attached to the lifter.  The massive robotic arm eventually grabbed the Xeno and killed it.

That massive arm is what through the lifter out of balance.  Tennessee even said to Daniels after she ordered him to release it that the arm was going to throw the lifter off balance.  

That is what we are seeing in the movie.  After the Xeno died, the lifter was brought back into place and locked down.

Yup! joylitt and I Moon Girl are right. While the cargo lift is in motion the crane is meant to be stowed. The crane is just for loading and unloading cargo while the lift is landed. Releasing the crane set the lift off-balance and made it really difficult for Tennessee to compensate.

Yeah. And the fact the the alien couldn't evade the claw is moronic

For Close Encounters I think it is a leap of faith on behalf of Daniels. She assumes that the xenomorph is going to feel threatened and attack the crane, as it it was another beast maybe. Of course it is too much assuming, because she just met the xenomorph.

Yea but it was unstable way before the crane was deployed!

I mean it narrowly misses several columns, Tennessee says he's beginning his ascent and he it crashes into and scrapes along the roof of the temple, then comes down the other side, almost at ground level, all before the scene with the crane/grappler.

And yea, the alien makes a point of jumping into the claw and attacking it.

Actually it is explained at one point in the movie; Daniels, Tennessee and Upsworth deliberate about whether the cargo lift can work or not for what they intend to do. Tennesse is very skeptic about it. I think its simply a vehicle that is not good  for maneuvering.

The cargo lift had reduced maneuverability as it was meant only to transfer the heavy machinery from the ship to the ground. It was basically a platform with 2 engines at the stern and 4 vertical thrusters at the corners. Plus the cargo crane. It was not designed to maneuver in a city or a plaza packed with statues. The controls of the cargo lift were also very basic in design to allow easy maintenance without some electronic spare parts. Tennessee was actually struggling to maneuver the cargo lift due to said reasons even though he was a good pilot.

The Protomorph attacked the crane because it threatened to push him off the platform. And Daniels used the crane because she was out of ammo and also had to distract the alien who was bumping his head into the windows and any crack was dangerous when the cargo lift would have been out of the atmosphere again, they did not have the suits with them. 

Yes. As I recall it, the Protomporph had a bit of a snarl at the opening crane mouth before he had a go at it. Maybe not the smartest of Aliens, his aggression got the better of him.

Yea if you slow it down, it jumps into the jaws, begins clawing at it and whipping it with it's tail

What the eff lol

I agree with the questioning in a general sense too but alas it's just nitpicking but I'll bite. When she grabs and traps the xeno it's actually kinda centered still over top the lifter and not massively off balance! Why does she know to MOVE the crane arm WAY out the side to SQUISH the xeno=so the plot could continue with the lander now being off balanced & out of control=more action. To the point of the thread, it's meant to haul mega heavy STUFF into high gravity so why is it struggling with just 600 pounds of human/Android and an extended crane arm? My only guess was for it making sense was the lifter was only used for low gravity outer space repairs but then I don't see how that massive Colony ship was going to scream into an earthlike atmosphere and land without a runway or busting up into pieces? Maybe it entered the colony planet and broke into sections with giant parachutes. Not bad action but when Daniels is shooting from the winch rope and then briefly running/dragging on the ground while still on the rope and still holding onto the gun was cringeworthy thus belonging to Micheal Bay film.

also, some of the time, the xenomorph was completely covering the piolits veiw of his surroundings. imagine driveing a car with a xenomorph on the hood. i imgine that you wouldent be driving perfectly.