If you've completed an ITI (Industrial Training Institute) course and then pursued a lateral entry into a Diploma in Architecture Assistantship, you may be eligible for admission to further studies, such as a Bachelor's degree in Architecture (B.Arch) or related fields. However, specific eligibility criteria can vary depending on the institution and the course you wish to pursue.

Here are some general points to consider:

1. Lateral Entry Admission : If you completed your diploma through lateral entry, you generally have the same rights and qualifications as those who completed the diploma via the regular entry. This means you should be eligible for further studies, provided you meet the other admission criteria.

2. Eligibility for B.Arch : For admission to a B.Arch program, you generally need to have completed a 10+2 (with Mathematics as a compulsory subject) or a 3-year diploma recognized by the state or central government. You would also need to pass the National Aptitude Test in Architecture (NATA) or another entrance exam specified by the institution.

3. Admission to Other Degree Programs : If you're not looking to pursue a B.Arch but another degree or course related to architecture, the eligibility criteria will depend on the specific course and institution.

4. Check with Institutions : It's crucial to check the specific admission requirements of the institutions you are interested in, as they may have their own criteria regarding lateral entry diploma holders.

If you are asking whether your diploma qualifies you for further admission or employment, it’s advisable to contact the admissions office of the specific institution or consult the official guidelines provided by the education board or university you're interested in.