In Lightroom: Adjust one photo the best you can. Play with white balance, tint. If you want, you may perform other adjustments that yo may want to apply to all the photos. I suggest sharpening, noise reduction and lens correction (if all the photos are taken with the same lens and at the same focal length). Contrast and tone curve. Spend enough time with that one photo to get it really right.

Now copy the settings (in windows [CTRL]+[SHIFT]+[C]) or vía the "Photograph" menu. Then, go to the grid viev (press [G]) and select all the other photos and paste the settings. (Pressing [CTRL]+[SHIFT]+[V] or right-click any of the selected photo and look for the "Paste Settings" in the pop-up menu.

When you copy the settings a pop-up dialog will let you choose which settings to copy. Only the checked settings will be copied and applied to the selected photos.

Now just go review every photo and make sure any adjustment is not overdone or under-done. The time you gained by pasting the settings will give you enough advantage to take this last step with patience.

Sync or Auto-Sync is another feature that will have a similar effect. You can select several photos (all of them if you want) then go to the develop module and activate the Sync switch. Now every setting that you make to the current photo will be applied also to all the selected photos. Deactivate the switch when you finish doing general settings and before you proceed to fine tune individual photos.

The aim is to do one time the setting that will make MOST PHOTOS RIGHT, and ideally, only a few of them may need a bit of further adjustment.

IF white balance and other non-local settings are not enough to propperly compensate the background the way you want, you can try with a local (brushed) setting. Local settings (brushes and gradual filters) can also be copied to all the photos, the difficult part may be that not all your subjects may fit on the same mask, so this is a more risky option and may not be really applicable to your case.

If ALL of your photos have the same composition, the same number of people in the same position. then you can go this route. Apply a brushed adjustment to one photo, but use the feathering of the brush so that the mask gets "thinner" towards the subject and thicker away from it. This will actually create a "halo" surounding your subjects, but if the brushed adjustment is feathered enough, and not overused, the result may be rather pleasing.

To whiten the background, based on your example, the brushed adjust shall augment exposure, reduce saturation, change temperature and tint, reduce contrast, reduce clarity and sharpness. Play with all of them until you find pleasing results. Then copy/paste settings making sure you select "Local Settings > brushes" in the Select Settings dialog.

If your photos have different compositions, work them in groups. Even if you have to do a little re-painting of the adjustment mask, having it smartly applied to all the photos at once will save you lots of time, and luckily enough, you wont have to edit the mask of too many photos.