I had two Minecraft instances taking turns hosting and connecting to LAN multiplayer sessions, a Win10 box using Java 1.8_71 32bit from Oracle, and a MacOSX 10.11 box using the Java (1.8.0_60 64bit) bundled with Mojang's mac launcher (v 1.6.48).

With the Mac hosting the session, the Win10 box is able to connect. However the Win10 box cannot host the Mac. I've pasted the launcher error message below.

After uninstalling 32 bit JRE on win10 and using 64bit JRE, the problem did not reoccur. If connectivity between 32bit and 64bit Minecraft instances is not supported, please close this ticket.

[12:25:56] [Client thread/INFO]: Started on 52727
[12:25:56] [Client thread/INFO]: [CHAT] Local game hosted on port 52727
[12:26:03] [Server thread/WARN]: Can't keep up! Did the system time change, or is the server overloaded? Running 2137ms behind, skipping 42 tick(s)
[12:26:03] User Authenticator #1/INFO: UUID of player skylander_guy is 6fc3a710-cd4b-4ff3-a1fd-a3c5f95a447a
[12:26:03] [Server thread/INFO]: skylander_guy[/10.0.1.5:61550] logged in with entity id 1039 at (-300.3389589176815, 98.0, 328.27040370210227)
[12:26:03] [Server thread/INFO]: skylander_guy joined the game
[12:26:03] [Client thread/INFO]: [CHAT] skylander_guy joined the game
[12:26:07] [Server thread/ERROR]: Encountered an unexpected exception
java.lang.OutOfMemoryError: Java heap space
at gp.<init>(SourceFile:32) ~[16w05a.jar:?]
at lu.c(SourceFile:127) ~[16w05a.jar:?]
at lu.a(SourceFile:60) ~[16w05a.jar:?]
at lv.a(SourceFile:226) ~[16w05a.jar:?]
at mm.a(SourceFile:274) ~[16w05a.jar:?]
at mm.c(SourceFile:330) ~[16w05a.jar:?]
at mm.a(SourceFile:160) ~[16w05a.jar:?]
at md.b(SourceFile:116) ~[16w05a.jar:?]
at md.c(SourceFile:62) ~[16w05a.jar:?]
at ek.a(SourceFile:232) ~[16w05a.jar:?]
at ma.c(SourceFile:187) ~[16w05a.jar:?]
at net.minecraft.server.MinecraftServer.D(SourceFile:642) ~[16w05a.jar:?]
at net.minecraft.server.MinecraftServer.C(SourceFile:552) ~[16w05a.jar:?]
at byl.C(SourceFile:154) ~[16w05a.jar:?]
at net.minecraft.server.MinecraftServer.run(SourceFile:456) [16w05a.jar:?]
at java.lang.Thread.run(Unknown Source) [?:1.8.0_71]
[12:26:09] [Server thread/INFO]: Stopping server
[12:26:09] [Server thread/INFO]: Saving players
[12:26:14] [Server thread/INFO]: ziggurism lost connection: TranslatableComponent{key='disconnect.genericReason', args=[Internal Exception: java.lang.StackOverflowError], siblings=[], style=Style{hasParent=false, color=null, bold=null, italic=null, underlined=null, obfuscated=null, clickEvent=null, hoverEvent=null, insertion=null}}
[12:26:14] [Server thread/INFO]: ziggurism left the game
[12:26:14] [Server thread/INFO]: Stopping singleplayer server as player logged out