Unless there's a particular reason to adopt continuous numbering, you should start each list, within an appendix, at number 1.
In many academic works there is no direct connection between the contents of the first appendix and the second one. For example, a study might be based upon interviewing members of the public. Appendix 1 (or A) could list the questions which were asked, from 1 to 20, but Appendix B might contain a list of references to other works. It would be illogical to start that list at number 21, as the items in that list are unrelated to the interview questions.
The only time that numbering should be continuous would be where it was clearly logical to do so. For example Appendix 1 might list the questions in an interview which were asked about respondents' home circumstances, from 1 to 10. If Appendix B then listed the succeeding questions (about, say, the respondents' academic qualifications) from the SAME interview it would be logical to commence the numbering from 11.
Chris