*whistles low* wow, this was posted a long time ago... but for the sake of if anyone else has this problem and looks at this thread in the hopes of finding an answer at the bottom, I'll respond anyway...
are you trying to double click lost.exe or lost.bat while dosbox is open? I dunno, that's what it sounds like you're describing. If that's the case, you need to actually open it from dosbox, not open it from the folder. It won't work that way. Dosbox doesn't make the files usable in general, it makes them usable in dosbox.
Anyway, make sure that you are mounting the hard drive and the cd drive correctly. For WinXP, here are my settings that I have to automatically run at dosbox's startup:
MOUNT C C:\SIERRA\LOST
MOUNT D E:\ -t cdrom -USECD 1 -ioctl
C:
LOST
That starts up LIT. If it still doesn't work, download the patch (there's a link on the forum somewhere). If all else fails, get a newer version of dosbox.