So at £16,000 thats about £1200 a month? Outside of the £450, what are you spending on other expenses - your ‘essentials’ like food/drink/etc, and more fun things?
Have a look at what you can legitimately save once all those figures have been accounted for too.
On the LISA front, these are a great mechanism to get a wodge of free cash, if you can afford to tuck the money away for an undetermined amount of time, and if you don’t want to buy before the LISA matures. (i.e, more than a year away).
Personally, with my LISA, I save what I can through the year and contribute to it just before the annual cut off - that way I still have the money if I need it ‘in year’.
On how aspect, once you’ve got your monthly budget sorted, I personally just chuck the savings into a Cash ISA pot in Monzo; it’s growing, it’s locked away, but I can access it easy enough. Other good suggestions would include a Marcus account too - which I think still has market leading interest, and its easily accesible.
While you’re saving though, my personal suggestion is to think of the ‘opportunity cost’ of buying a house at the moment - does tying yourself into a 25+ year mortgage right now make sense; are there any skills development that you want/need/might consider that would enhance your savings rates in future, etc? Long term do you want to live where you would buy.
Good luck on the journey 
Edit: Oh and just to add - personally, I would also be aiming to grow an emergency fund of some sorts (common wisdom says 1-3 months salary) - so at least if something does happen, you have a slush fund you can draw from if needed. Or rather, just consider ‘protecting’ some of your savings as your building your deposit.