The android error just means the server isn't available at the moment - I think sometimes they take it down for updates or maintenance or something. Give it a while (could be hours, could be a day), and it'll come back.
When I get that error, it's when I try to sync, but I can still access the content (directory, etc.), I just can't sync. So, can you access the already-downloaded stuff, or not even that? Is your LDSTools somehow set to automatically sync when it starts? (Can't see a setting like that, but maybe having a PIN does it - I don't have a PIN, and I'm not someone who has access to extra information, like Bishops and Ward Clerks.)
If it does automatically sync, is there a setting somewhere for that? Do you have a PIN set up? (Please don't tell us your PIN - I know I shouldn't have to say that, and no offense, but sometimes people answer that kind of question by giving the PIN / password.) Do you have a calling that gives you access to extra information?
I don't really know the answer if you can't view LDSTools without the internet and the church's sync server available, but these are the kinds of questions I'd ask to figure it out...
NOTE: If you can use LDSTools without the internet, then after getting this error, you could disconnect from the internet, open LDSTools, and then reconnect to the internet without restarting LDSTools, then it shouldn't try to sync again.
FWIW,
Liz