Veselí nad Lužnicí, Kardašova Řečice, and Novosedly nad Nežárkou are all indeed in the same area and not very far from Třeboň. U Lapicu simply means a house or place where the Lapic family lived (The Lapic’s House). There still many houses in the Czech Republic called U, followed by the name of a family, even though the family hasn’t lived there for decades or even longer.
České Budějovice is a city of over 100,000 people about 30 km west of Třeboň. You may try writing to the individuals you found in the phone book. If you’re lucky you may get an answer, but generally most people in the Czech Republic are not interested in genealogy and have no idea how to go about researching their ancestors. You can try writing in English (it’s now one of the languages taught in school) or in German, which many older people understand.
However, if you’re really serious about researching your ancestors, I would recommend hiring someone in the Czech Republic to do the research for you. The parish registers for the three places should be at the State Regional Archives in Třeboň. The Archives will not do any research for genealogists so it’s a waste of time contacting them. I suggest you visit the Small Towns, Oxford Junction, Iowa web site. They have a section with names of Trebon Archives researchers for hire. The link is http://www.geocities.com/oxfordjct_suchdol/trebon_archive_re...
Good luck with you research.