Here are some pictures I found on how to lift a heavy box. Is this correct technique? Mainly I am trying not to hurt my lower back.
This idea that the "correct" way to lift involve getting your hips as low to the ground as possible is something that has historically been taught, but has no evidence behind it. It's more of a dogma than a correct technique.
Martimo, K.-P., Verbeek, J., Karppinen, J., Furlan, A. D., Takala, E.-P., Kuijer, P. P. F. M., Jauhiainen, M., & Viikari-Juntura, E. (2008). Effect of training and lifting equipment for preventing back pain in lifting and handling: systematic review. BMJ, 336(7641), 429–431. https://doi.org/10.1136/bmj.39463.418380.be
"There is no evidence to support use of advice or training in working techniques with or without lifting equipment for preventing back pain or consequent disability. The findings challenge current widespread practice of advising workers on correct lifting technique."
Regarding the deadlift addition that was added in a later edit, the statement "[arms perpendicular to the back] means that all the weight of the package is converted to dangerous shear forces on the back" is not true. There's nothing special about a situation in which the arms are parallel to the back, and shear forces are present in almost all loadings of the back and are not inherently harmful.
"The neutral back lifting posture has been found to be better overall than a rounded (opposite of arched) back in minimizing L5/s1 compressive forces and ligament strain. Therefore, a normal lordotic lumbar spine position is superior to a rounded back for avoiding injury to vertebra, disks, facet joints, ligaments, and muscles of the back. In addition, the low back muscles are capable of exerting considerably higher forces when the back arched rather than rounded." (1)
"It has been observed that 85% to 90% of all intervertebral disk herniations occur at the disk between the lowest two lumbar vertebrae (L4 and L5) or between the lowest lumbar and the top sacral vertebra (L5 and S1)." (1)
From this we can conclude that we should lift with a "straight" back if possible. And in order to keep a straight back we must hinge at the hips.
But why do the herniations occur at the bottom of the back and not further up the spine? Let us model the spine as a rod flexing from the force from the weight transmitted trough our arms and shoulder. This is similar to the cantilever beam problem in static analysis:
In our case the sacrum is the fixed end and our shoulders are the free end where the force is applied. From the figure it can be seen that the bending moment at a position x where x=0 is fixed end and x=L is free end is: M=(L - x)W This moment is clearly largest near the fixed end. Likewise the bending moment from lifting a weight is largest in the lower vertebraes (L4 and L5).
This bending moment is opposed by the erector spinae muscles. However: "The back muscles operate at an extremely low mechanical advantage because the perpendicular distance from the line of action of the spinal erector muscles to the intervertebral disc are much shorter (about 5 cm) than the horizontal distance from weights to the disks. As a result, the muscles must excert forces that frequently exceeed 10 times the weight lifted". (1) This is illustrated here (from Physics in Biology and Medicine, Paul Davidovits):
In order to save our backs we should therefore outside the gym seek to minimize the torque from the lifted weight at the sacrum in case our erector spinae should not be strong enough. Inside the controlled environment of the gym we should strengthen our erector spinae by stressing it (deadlifts).
In another question I have found that we should try to lift as upright as possible and with shoulders as far as possible in front of weight. However it seems these criteria oppose each others. The first leads to a squat and the second to a deadlift.
How do we do this in practice? We use a lift somewhere between a squat and a (sumo) deadlift. A sumo stance causes a more upright back position. And we try to get our hips as horizontally close to the center of mass of the box as possible. It is important to notice that the height of the hips does not matter (2):
Regarding the first person in the original question: the feet must be firmly planted in the ground in order to be stable. He is clearly limited by his ankle mobility and need to take a wider stance and turn his feet more out. The second person has a good lift.
(1) Essentials of Strength Training and Conditioning, Biomechanics chapter, NSCA