The log shows that the Server suddenly blocks for about one minute.
See for instance your latest log between 02-Apr-18 14:34:46 and 02-Apr-18 14:35:49.
It is really a block, because the 2-second periodic LightstreamerMonitorText lines are also missing.

The most common explanation is a major garbage collection. However, the free heap is always very large; this is strange.
Please ensure that you have set the recommended GC options in the command line in LS.sh or LS.bat, that is:
-XX:MaxGCPauseMillis=1000
and, just in case, also
-XX:+UseG1GC

About the memory, you should ensure that the amount of memory allocated to the JVM is not larger than the available RAM.
The JVM should be smart enough not to use more memory than available;
but have you set a -Xmx setting explicitly in the command line in LS.sh or LS.bat?
Or does the JVM share the avaiable memory with other memory consuming processes? For instance with some of the Remote Adapters?

By the way, this issue seems not related with Remote Adapter problems.
However, when the Clients and the Server try to overcome the block, they put a lot of pressure on the Remote Data Adapters, which seem not able to cope with the amount of subscription requests and begins to answer too late.
You may evaluate increasing the
<param name="timeout">
element in the <metadata_provider> and <data_provider> blocks in adapters.xml.