I would say it depends on whether you are doing normal FT or accelerated; I did normal FT and it was difficult but definitely possible.
I started the LPC and signed up for pro bono opportunities straight away as they ran before VS deadlines (and are really competitive for this reason). They gave me lots to write about in apps and discuss in interviews, in addition to university stuff. I also attended lots of virtual insight evenings and open days which massively bloated my diary. I then got 6 apps in before Christmas. The next term was seriously tough - with having at least one AC/interview for 5 of those apps alongside exams - but again possible if you're organised.
I think the trick is to study smart on the LPC; if you are going to ULaw, make use of recorded workshops as consolidation and don't get bogged down making ridiculously long notes from the textbooks. Try and go to every workshop and make good notes in the workshops themselves