generally when i pm a truck if i have to adjust the chains i just try to figure it in with the pm labor if its a quick adjustment. Sometimes i have to compensate and spread extra time across the day if it takes too long. My employer likes for us to create a charge for doing so if it takes more than 15-20 mins. Same with blowing off the lift and radiator or checking the battery and having to add gallons of water to an electric truck battery.
I try and use the 30 minute rule, if any extra stuff i do requires me to take up to or beyond 30 minutes then the customer gets charged for it over and above the PM flatrate charge.
Being it only has to be done every so often they usually don't gripe too badly about it.

As for how to measure, we do use a chain guage which is a go/nogo guage. As for the pitch it is usually etched on the side of the links. Most of the average sized chains on 3000 to 5000 lb lifts use something like BL40 multi leaf chain.
And yes 1/4 to 1/2 in might be ok but when i worked for yale they told us to have mast vertical and adjust the forks 1 in off the ground (measuring between the heel of the fork and ground)
If you have to adjust the inner channel chains that's pretty simple, just making sure the channels are even at the top of if there are stops make sure they are not sitting dead on the stops crushing them.

What kind of lube?
I like using endura lube or permatex chain and cable lube. They both tend to solidify when the air hits it so it doesn't run too bad except for in the hot summer, then you have to be careful and spray it on light.