This may be limited by the number of departments I've looked at, but almost every one of them requires at least a full year of graduate level analysis before you start taking graduate level probability theory. Many of the same programs also require passing the standard Algebra, Analysis, Topology qualifying exams before you start doing applied work (prob/stats) towards your PhD.
That being said, I'd considering doing as much of a pure math focus as you can do as an undergrad to prepare yourself for passing your qualifying exams in grad school ... while taking at least a single prob/stats course (or many if you can fit it into your schedule) to give yourself a taste of what the field is like ... even if it's just at an introductory level.
Like many of the others said as well, becoming a "lecturer" is much easier said than done. These are some very rough (educated guess) numbers that may help illuminate your current view of the field you want to be getting into:
Let's say a prof has a 35 year career and they only advise one student at a time for a period of 5 years. They have graduated 7 PhDs by the time they retire ... only 1, maybe 2 of them (due to university / population growth) will be hired in their place. Some may go on to teach at non-PhD granting institutions, and others will go into industry, so these things must be factored in, but even still, positions are much lower in number than the number of qualified PhDs in the applicant pool to fill them.
That being said ... factor in a plan B (or C, or D) now, while you're young and have loads of options. If academia is still what you think you want to do, work as hard as you can if you actually want a teaching position: straight As, as much pure math as possible, and even more applied stuff if you can fit it in your schedule = you'll have a much better shot at making that happen, but even then there's still elements of luck, timing, and politics to deal with.
Literally cryed I laughed so hard.
