It's been a long time since I made lemon meringue pie as I like pies too much and don't need the extra sugar and fat calories. What always worked for me was to partially blind bake the crust first and then after removing the beans, brush the bottom with egg white before baking another 5-10 minutes.
Blind baking a crust is done by getting the crust ready in the pie plate, then covering it with aluminum foil or parchment paper before filling it with small beans. The beans weigh the crust down so none of it forms bubbles while baking. (Easy to lift the corners of the paper up with beans in it.) I'd take the beans and paper out, brush the inside of the crust with beaten egg white and finish browning it in the oven.
The very thinly coated egg white wash further seals the crust forming a water-resistant barrier to the moisture of the filling. I know most recipes say to add hot filling to the crust but I found that waiting til the filling had cooled to warm instead helped prevent soggy crust. My reasoning is flour products soak up moisture faster with hot liquids than those that are merely warm.
One further tip. Cornstarch (called cornflour in the UK) isn't as effective in acidic foods so a cornstarch thickened lemon pie filling tends to separate somewhat the next day, releasing some of the water. Arrowroot flour (powder) is best for thickening acidic food but not always avaiable and more pricey. Tapioca flour works almost as well and is much cheaper. I won't use cornstarch to thicken acidic food - it's best for milk-based foods.