Finally I change mysql setting and set "Maximum Run Time (seconds)" on 300 and AOE Scheduler on 400 an its works fine (without errrors), but I've got one more problem.
In logs I see:
2015-12-01T10:20:02+00:00 DEBUG (7): LiteMage: [litemage_walker] load url count = 0
2015-12-01T10:20:02+00:00 DEBUG (7): LiteMage: [litemage_walker] no url list available for warm up
but most of website is not getting from cache.
Accept-Ranges bytes
Cache-Control no-store, no-cache, must-revalidate, post-check=0, pre-check=0
Content-Encoding gzip
Content-Type text/html; charset=UTF-8
Date Tue, 01 Dec 2015 10:41:29 GMT
Expires Thu, 19 Nov 1981 08:52:00 GMT
Pragma no-cache
Server LiteSpeed
Set-Cookie frontend=877dar3f9r7k46upch8dvcmfa4; expires=Tue, 01-Dec-2015 20:41:27 GMT; Max-Age=36000; path=/; domain=sklep.almach.pl; httponly
Transfer-Encoding chunked
Vary Accept-Encoding
X-Frame-Options SAMEORIGIN
X-Powered-By PHP/5.5.30
After opening it once, it's getting from cache again:
Accept-Ranges bytes
Cache-Control no-store, no-cache, must-revalidate, post-check=0, pre-check=0
Content-Encoding gzip
Content-Type text/html; charset=UTF-8
Date Tue, 01 Dec 2015 10:41:55 GMT
Expires Thu, 19 Nov 1981 08:52:00 GMT
Pragma no-cache
Server LiteSpeed
Transfer-Encoding chunked
Vary Accept-Encoding
X-Frame-Options SAMEORIGIN
X-LiteSpeed-Cache hit,litemage
X-Powered-By PHP/5.5.30
In litemage cache settings I have default TTL.