Adding a corset to a lace back wedding dress

Discuss that with your seamstress

I worked in bridal for three years. In terms of whether it's possible, it looks like the lace is just an overlay, and the underlay fabric looks like it would be sturdy enough to support the tension of a corset (based on the boning already present). In terms of whether or not the look of the lace up on the sides and the back would be too much, that's really up to you! If it would make you feel more comfortable and less worried on the day of it might be worthwhile. Regardless, I would take it in for alterations to see what can be done so that you don't have to stress about it!