Unless the records you seek are relatively recent, i.e., since Lithuanians independence (1990), local churches made such records but they were corralled by the Soviet Union into the central Lithuanian Historical Archives. Records in the Archives can be accessed by certain relatives, but privacy concerns limit access to records less than 100 years old, i.e., after 1910.
Since the online phone book for Lithuania does not list any name beginning with Lasis-, Lazis-, or Laziz-, it appears that you are looking for old records, i.e., pre-WWII perhaps. The Polish or Slavic spelling of this surname points to a Lithuanian spelling like Laziskas, Lasiskas, Lasizkas, Laz^is^kas, Las^is^kas, or Las^iz^kas. But none of these show up in either of the two online phone books.
However, the surname Lasickas does show a few listings, so my guess is that this how the surname would be spelled. This name would be pronounced lah-SITS-kahs.
It might be helpful to know a bit about the Lithuanian alphabet and how some of its letters are pronounced. The letters "c", "s", and "z" have two forms in Lithuanian, both of which are pronounced quite differently. One form of these letters has a little mark or birdie over them (often typed "c^", "s^" or "z^); the other does not.
The letter "c" with a birdie is pronounced only "ch" as in the English word "church". The letter "s" with a birdie is pronounced "sh" as in the English word "shout." "z^" is pronounced "zh" as in the English word "azure."
The unmarked letter "c" is pronounced, surprisingly for many English speakers, as "ts" as in the name "Vince" or the word "bits." Lithuanian uses only one pronunciation for each letter in its alphabet, unlike English which uses "c" for the sound "s" as in "cent" or "city" as well as for the sound "k" as in "count" or "Catholic". That "k" sound is rendered in Lithuanian never by "c" but always by "k". So "c" in Lithuanian is "ts" and "c^" is "ch."
The unmarked letter "s" is pronounced the same as the English "s" in the word "solid" and, as noted above, the Lithuanian "s^" is "sh". There are no other pronunciations to each of these letters (all the birdie marked letters are considered separate letters of the Lithuanian alphabet).
The unmarked letter "z" is pronounced the same as the English "z" in the word "zoom", but when it has a birdie it is "zh" as noted above.
So the Lithuanian surname Lasickas is not pronounced "lah-SIH-kahs" but "lah-SITS-kahs". My maternal grandfather's surname was Kuckailis, pronounced not as koo-KAI-lihs but as koots-KAI-lish. He changed it by dropping the ending (very common among immigrants to English speaking countries) and using a phonetic spelling (spelled as it sounds): Kutskel.
The Lithuanian address for the church in Krivonys (Kais^iadorys district) is:
S^v. Antano Paduviec^io
Krivonys, Z^asliu ps^t. (ps^t = pas^tas, post office)
LT-56397 Kais^iadoriu r. (r. = rajonas, district)