Pokemon Let's Go may be aimed at the young audience and casual gamers but it can be changed a little to make it a little harder and a bit more of a challenge. Keep in mind these few tips won't make the game Dark Souls levels of hard but it may make it feel like more of a traditional Pokemon game.
Don't use your starter
This first tip may come as a surprise to some and even a disappointment to others. The easiest way to make the game harder is to box your starter as soon as you can. Having your starter in your team and on your shoulder/following you increases its EXP gain and can make it over powered quite quickly.
Due to the way you gain EXP from catching other Pokemon your starter is going to have a huge head start and it will be much quicker to beat the early trainers and continue this spiral of higher EXP gain.
Don't Walk with any Pokemon
In a similar fashion this tip will take away a core part of the game. The game will reward you for walking with your Pokemon both in game and in the Pokeball Plus. If you use this amazing new feature you are putting yourself at a huge advantage that will make the game incredibly easy for you.
In the same vein as the first tip you will gain EXP for your Pokemon much faster through the use of the Pokeball plus and through having them out of their Pokeball in-game. If you wish for the game to feel more like the old school traditional games you would best avoid this feature.
Pokemon Let's Go has made grinding incredibly easy for a Pokemon game and such needs to be avoided if you want the game to feel like the old days. Everytime you catch a Pokemon your entire party gains EXP meaning that if you grind you'll be miles ahead of where you should be. It's very easy to over level in this game and it really can take the fun out of it.
If you wish to catch every Pokemon in one play through I would recommend having a rotating team and work on getting all Pokemon caught to decent levels before moving onto other areas.
At the end of the day you can always create multiple saves or play through the game multiple times to experience everything on offer. I recommend avoiding playing in "hard mode" until your second playthrough as the game has lots of great features you will avoid via "hard mode". You really should walk with your Pokemon and play with your Pikachu or Eevee. It's a tonne of fun and done really well.