i am not a tech, nor am i overly experienced but i recently purchased a front suspention and had the same questions, This is what i think i figured out….
Suspension "bobs" (bounces up and down) when pedaling up a hill. This "bob" eats up some of the energy you are putting to the peddles. Locking out the suspension keeps the shock or shocks from bobbing and basically turns your suspended ride into a heavy rigid bike. That said most "lockouts" do not totally lock the shock. For example my 90mm Reeba (dual air) when locked out only travels 10mm to 20mm (that might not be accurate but you get the point). I am not sure how lock out affects a coil suspension but i assume it is similar. This reduced amount of travel is supposed to improve efficiency while pedaling up hill while still absorbing the smaller bumps and roots in the trail.
It seems to me that 90% forks have some sort of lockout. Some of the lower end fork do not have lockout and also forks that a strictly made for downhill rigs with 8+ inches of travel.
The rear shock, to the best of my knowledge, depends on the suspension and linkage design. Some companies claim that their design is effective on climbs with no need to be locked out.
My Experience: Like i said i have a Reeba Race on my bike. It has a little lockout lever mounted on the handlebar, I honestly do not use it.. I do not find any difference while climbing with it on or off. and half the time i forget unlock it when i am heading back down the hill. That said i am riding in Nebraska so aaaaa no mountains. the climbs i reefer to are relatively short gradual ordeals. I can not attest to a steep 30 minute technical climb on the side of a mountain. also i do not race, so going slow uphill dose not seem to bother me.
good luck