This is not possible directly through a desktop shortcut, but there are some other options:

- Use a .bat file that fills in the search syntax with the date:

@echo off
set X=
for /f "skip=1 delims=" %%x in ('wmic os get localdatetime') do if not defined X set X=%%x

set DATE.YEAR=%X:~0,4%
set DATE.MONTH=%X:~4,2%
set DATE.DAY=%X:~6,2%

start /b "" "C:\Program Files (x86)\Laserfiche\Client\LF.exe" -LREPOSITORYNAME -S"{[General]:[Date]<=\"%DATE.MONTH%/%DATE.DAY%/%DATE.YEAR%\"}"

Replace REPOSITORYNAME with the name of your repository and General / Date with the template and field to search on. Date calculation in batch files is hard to get right, I found this date calculation method here.

If you need more complex date calculations such as within the past two weeks, you can use powershell or vbscript to do the date calculation and launch the client with the -S parameter. For more information on the command line interface, see the online help.

- Use a saved search. Obviously not as user friendly but it is less error prone.