I have a Java applet, designed under 32-bit JDK (1.5). When deploying it on a new MacOS (10.7) it runs incorrectly - because 64-bit JRE is preferred by default in this syste
So, the problem is kind of solved, if anyone is interested.
For an applet it's impossible. It is possible to launch JVM in 32-bit mode with the use of Java Web Start. But with current (Java SE 6) implementation, JWS is less convenient than applets, because of an absolute 'codebase' field in config file, which limits the deployment of an applet/application.
It seems that problem is in JRE implementation - my program really has very limited system-specific parts, and no part that depend of bitness. Would continue testing, to localise a problem for a bug report :)