We have been having a bit of a nightmare this last week with a business critical XPage application, all of a sudden it has started crawling really badly, to the point where
Try to get more info about state of your server and application.
Hardware troubleshooting is summarized here: http://www-10.lotus.com/ldd/dominowiki.nsf/dx/Domino_Server_performance_troubleshooting_best_practices
According to your experience - only one of two applications is slowed down, it is rather code problem. The best thing is to profile your code: http://www.openntf.org/main.nsf/blog.xsp?permaLink=NHEF-84X8MU
To go deeper you can start to look for semaphore locks: http://www-01.ibm.com/support/docview.wss?uid=swg21094630, or to look at javadumps: http://lazynotesguy.net/blog/2013/10/04/peeking-inside-jvms-heap-part-2-usage/ and NSDs http://www-10.lotus.com/ldd/dominowiki.nsf/dx/Using_NSD_A_Practical_Guide/$file/HND202%20-%20LAB.pdf and garbage collector Best setting for HTTPJVMMaxHeapSize in Domino 8.5.3 64 Bit.
This presentation gives a good overview of Domino troubleshooting (among many others on the web).