If you are at 45 seconds using Fridrich, I don't think your main problem is lockups. Just keep practicing the method for now, but obviously, on F2l, don't go as fast as physically possible on each pair.
Get a DIY at some point, that can eliminate some lockups, depending on the cube you choose. In my experience, type As lockup the least, Cs are a good balance of speed and smoothness, and Ds are very fast but lockup a lot.
Also, I'm assuming you don't use one look OLL and PLL, so I think you should just keep learning and practicing the method.
Practicing specific algorithms, as fast as you can, to help you get used to them will avoid lockups on the LL, in particular, in my opinion. Try that when you get your DIY.