Lateral entry

Yes, you can definitely get admission for your engineering graduation after completion of your Diploma. When you complete Diploma, and then seek admission directly into the second year of engineering, it is called as a lateral admission. It is the accepted norm in Maharastra State and you can get admission under this category definitely. BE or B.Tech is one and the same thing, and don't get confused by the nomenclature. Some institutes award B.Tech while others award BE, but both are exactly the same. I am attaching a link of the website of the Directorate of technical education of the Maharashtra government. By clicking on the link you will come to know the process and the complete information about this lateral admission.
http://www.dtemaharashtra.gov.in/index.html
Best wishes to you.

It is very nice to see that you are a sincerely studying for LEET examination of Jharkhand. It shows your sincerity for seeking admission in Engineering college, after completion of your Diploma. As far as the books are concerned I can advise you that the syllabus for LEET is basically the same as that for Diploma and hence your books will be good enough. However based on the syllabus you can Google for previous years question papers and you will come to know what type of questions are asked and also different publications which are offering books for this examination. As a counsellor of Shiksha, I cannot recommend book of the particular publisher, it is for you to decide which books to refer to. Best wishes to you.