I think you could continue your daughter in Lotus Lap till UKG and then look for a change. There aren't many established CBSE or ICSE schools in and around Dsnr/ LB nagar / Hayath Nagar. Choice is very limited.
You will find below schools in and around these areas.
Johnsons Grammar ( ICSE)-LB Nagar.....
RamaDevi Public School( ICSE) near Ramoji Film city which is quite far......
Below are CBSE schools :-
Akshara International School ( LB Nagar)-----
Edify world School - Balapur----
DPS- Nagergul - new school..........
Birla's Shloka School - Mansoorabad near LB LB Nagar - new school----------
Mount Litera Zee School- Hayat Nagar - ----
Little Flower- Uppal------
Johnsons Grammar- Uppal -----
Usually most of the schools start admission in the month of Oct/ Nov.
As you stay in Hayath Nagar, I think you could prefer Mount Litera Zee School. It is a good school and you could continue your daughter till Class X. My cousin's son is studying here and she is quite satisfied.
Pls see my reply to Aamvi for 'CBSE vs ICSE' in the below link.
The syllabus is vast in ICSE in higher grades and also the number of papers are more in Board Exams. If your child is in ICSE from the beginning, she wouldn't find it difficult in higher grades.http://www.parentree.in/India/Hyderabad/39548-hello-mickey-need-to-know-whether-icse-or-cbse-better
May be you could visit the above schools and