What happened to night trains Kiev-Lviv?

Schmechi, don't worry. The explanation is rather trivial. In Ukraine (and other ex-USSR countries) during last weekend of May happens annual train timetable schedule change (like second weekend of December in the rest of Europe). So currently simply not all the new timetables agreed and 'validates' (especially since UZ plans to introduce new express trains etc.). As soon as all the formalities will be agree then sales will open. As well you need to remember that only for some major trains sale opens 90 days in advance (and it is rather recent thing for UZ,btw), while for other it's usual for UZ 45 days in advance ;)

Btw, train #97 definitely won't run to Lviv from new timetable, also #91 will change the route, while #169 will be almost definitely substituted by faster (and new) Hyundai EMU

do not rely on e-kvytok it is not a very good website
Here's a list of all the trains between Kiev and Lviv, it looks like the 169 doesn't run during the EC, but there are many alternatives

http://www.uz.gov.ua/en/passengers/timetables/?from_station=KYIV-PAS.&to_station=L%27VIV&time_from=00&time_to=24&by_route=Search

do not rely on e-kvytok it is not a very good website

Why? As far as I know, e-kvytok (disregarding language issue and not problems with interface) is not just the only official website where you can purchase UZ tickets from, but also the only Ukrainian website with 'live' access to 'Ekspress-UZ' reservation system (thus depicts 'live' changes in schedule, price etc.).
While uz.gov.ua is official UZ website, but still it's an offline resource, so no 100% guarantee about up to date timetable or all the possible changes.

That's good news, although I wonder, why it is (theoretically) possible to book for this special period.... So let's wait again and let's hope it'll be possible to book in the mid of May...

although I wonder, why it is (theoretically) possible to book for this special period

What do you mean? That e-kvytok allows to choose date in June?

it'll be possible to book in the mid of May

Imho, better to try earlier, there is a good chance that in a week or two all the schedules will be in (at least some of them are already known, so it's just a matter of week(s) until rest will be as well, and thus sale will be 'open' for all)

Why? As far as I know, e-kvytok (disregarding language issue and not problems with interface) is not just the only official website where you can purchase UZ tickets from, but also the only Ukrainian website with 'live' access to 'Ekspress-UZ' reservation system (thus depicts 'live' changes in schedule, price etc.).

Even with knowledge of Ukrainian the website is quite useless to book tickets from abroad, one poster on here recently reported about it as it doesn't support the 3D card verification used in for example the UK.
From my own experience having tried to use it, it came up with only a few available places on the train I wanted, checking at the railway station it turned out there was much more available then what they showed on line. It is also extremely slow and very often just hangs leaving the user confused and thinking did I book (and pay) or not.

website is quite useless to book tickets from abroad, one poster on here recently reported about it as it doesn't support the 3D card verification used in for example the UK

I'm not trying to defend e-kvytok, but I think they fixed all the issues with 'foreign' cards like a year ago or so. At least I haven't heard about any troubles lately and know a few people who booked ok with non-Ukrainian cards.

it came up with only a few available places on the train I wanted, checking at the railway station it turned out there was much more available then what they showed on line

Strange, usually it happens vice versa, because at the ticket counter there might be some limitations on sale, while e-kvytok from the beginning operated surpassing any such limitations. The answer to your situation really depends on particular train and time of purchase, but there are quite a few explanations. For instance, at the moment UZ doesn't start selling ticket to all the carriages at once, but only a few. And when the number of free seats <8 (per carriage), then next carriages (all the seats) are released for sale. Also there are 'groups of tickets' that are being released certain number of days/hours before departure etc. Another explanation regards international trains on domestic UZ route, for them system doesn't see any free seats. So believe me, it's not always e-kvytok, there are plenty of other possible causes ;)

p.s. Ukrainian officials lately announced that they will introduce totally new system (substituting e-kvytok), promise was till the end of April, but might be too optimistic to believe in that

@Regarding credit cards: It seems, that http://www.e-kvytok.com.ua is not the only site, which have problems with foreign credit cards. I got the information, that credit card companies tighted their security conditions regarding Ukraine, so there are huge problems with e-business between Western countries and Unkraine. Direct payyment is nearly impossible, for instance all hotels had to be payed with (expensive) foreign bank transfer or I had to (postally!) mail them an additional form with my signature...

@Regarding http://www.e-kvytok.com.ua: I read in a fanzine, that a new reservation system should be launched on the 15th of May 2012. Supposedly it will also be in English... But mid of May is relatively late, so I wanted to try to buy them earlier in advance... Additionally I am in doubt, that everything will work fine right from the launch of the site. And finally a football fanzine is normally not the most confidential source for such kind of information...

Unless things are changing, I believe that the Russian and Ukrainian rail systems don't allow booking more than 45 days prior to departure.

Ruth