There are a couple work-arounds, but that might not make a difference for you. You dont specify what you mean by "very short time when i can play". If we look at the first CT raid, it takes about 18 minutes to complete once you start. On a healer class during prime time hours, your que would be less then 5 minutes(a little longer for dps, a little more then that for tanks) giving you a total of less then 25 minutes required to get the whole thing done(30 if you want to estimate high). If most days you can only log on for 15 minutes, this small commitment will still be a problem. If your play time is predictable(i can play from 12 to 1245 every friday and saturday), you could set up a group in advance so that when you log on everyone is already there and you just join and hit play. Removing the que time gets the run to reliably under 20 mins(20 mins in LotA is enough time to wipe once or twice and still finish). If your time is predictable and you have higher level friends you could set up an un-synced party to take you through. With unsync, the instance is probly clearable in 10-12 mins(this is an estimate, as ive never actually tried). The problem is you need 12+ players to unsync the first raid(you can try the 2nd and 3rd with less, but mechanics require 12 for the first one). Forming an unsynced LotA run would take awhile, so this would need to be set up in advance(probly by some higher level friends) to get you in and out in time.
The workaround for unpredictable play times without a lot of higher level friends who can be called on is a story skip potion. Paying to skip this content hurdle... isnt ideal. Beyond those ideas, i dont have anything aside from taking a break from the game and coming back when you have more time to actually play. But again, this is all based on not knowing exactly how much(or little) playtime you have. There are some people who would say playing an hour a day(as in one straight hour then logging out for the day) is very short, and i would tell them just to que up as soon as they got online and they could finish this over the weekend. If you literally have 10-20 mins now and then, instances will always be a problem.