Lake water, containing little salt, is comparatively innocuous to most electronic devices. If the battery had been removed immediately, to prevent electrolytic corrosion, the laptop would probably work after thorough, though gentle, drying, though a HDD probably would need to be replaced (an SSD should be fine, though).
Even with a battery in place, the notebook might be salvageable, not just the display. Rather than remove and test the display, try to fix the whole laptop:
- Remove battery, hard disk drive, DVD drive and loudspeakers, if practical.
- Dip the notebook in distilled water a few times.
- Repeat dipping, but in 90% or stronger ethanol or isopropanol.
- Repeat dipping, in a fresh ethanol or isopropanol bath.
- Gently but thoroughly air dry with warm (less than 60° C), dry air. Give it a week or two.
- Replace parts removed (though an HDD or DVD is unlikely to work after immersion).
Mechanical parts such as loudspeaker, HDD and keyboard might not work, or not work well, but replacement parts are inexpensive. You can operate the laptop without HDD using a live (bootable) USB with an OS such as Linux.