Yes! They can. To change the search type, invoke the Lynx Options Menu. The default keystroke for this is "o". On the menu is the line:
S)earching type : CASE INSENSITIVE(or CASE SENSITIVE if that is the current setting). Press "S" and then the space bar to change the setting. When the setting is the one you want, press the return key to accept it. You can save the settings using ">" if you want this to be the new default for your Lynx sessions. Press "r" to return to Lynx without saving the setting for future sessions.
Would you like to view the key bindings for the version of Lynx you are currently using? This won't work if you are not using Lynx, by the way.