Every year I try to complete the LS collection without spending money, not because I take issue with people who spend money (by all means do that if you so please) but because I can't afford it. I thought I'd make a guide for people in the same boat as myself. Last year I completed the full LS collection and I should have it done within the next week or so this year.
Make Tangible Progress
If you have the stubs to complete an easier team without diamonds (such as the Tigers or Marlins), absolutely do it. There's a few reasons why I suggest this. Number one, it removes stub temptation, you now no longer have the ability to burn those stubs on packs and have permanently dedicated them to the LS collection and secondly, it makes your goal seem more real. If I complete the 10 easiest teams, I'm still done 10 team and now have notable progress, this will help for your own motivation but also just helping you commit to a goal in mind.
Team Affinity
If you completed all of stage 1 and 2 right now you'd have over 300 TA (standard) packs and 60+ BIAH packs. In theory those packs would cost about 1.5M stubs, but let's be realistic, you won't earn that back without absurd luck. However, you don't need to, chances are (even with medium/decent luck) you can make 500,000. I recommend doing all of these and saving them to open at once, why? Because then after selling everything, you can do a big chunk at once and once again, not be tempted to waste stubs. This also doesn't include showdown or conquest packs too which you'd likely get along the way.
You probably need to invest
I only invest stubs about 2-3 times per year, but when I do, I go pretty much all out, amassing 150+ of the gold player of my choosing. Oftentimes, I'll spend a whole week immediately investing stubs in the player of my choosing after I get the stubs. Let's say the gold I want is 1800. Every time I get 1800 I place an order. Especially this year SDS has been generous with their diamonds, so it's not too risky and it's very high reward. Don't try to predict performance, it's too hard, instead look for players who are undervalued. For example, Marcus Semien has a decent shot at diamond, and is about 3,000 right now, I bought many of him just a few days ago at 1,800 because I saw that he should be higher based on his stats this year.
You might have to sell a boss
I sold my inning boss for stubs, and then used those stubs to invest. It may seem counterintuitive to sell the card you just worked hard to earn, but think about it. If you sell a boss early for say 100k, you can invest that into 50 golds of a player you think could get upgraded, if he gets upgraded, you quicksell the diamonds for 250k, and you buy back the boss (who's now even cheaper) for 70k. You just made 180k stubs just by being smart and patient. And the more you have the easier it is to make and invest in stubs.
Know your goal and take your time
If you really want to accomplish this collection whilst already being behind the eight ball, make sure you're dead set on it. It's easily obtainable, but also know it might not be right away. It's taking me about 2 months thus far, but with programs like TA1 and 2 both available right now, you could do this quicker if you really focus on it.
Some other things to try. If you're good at BR and it's profitable or if you can make and sell WS rewards to invest (I do neither of this because I'm not good enough to accomplish either quickly and efficiently). Flipping is a lot harder this year in general and harder than investing, but if you have the time and resources maybe give it a try.
will finish the drum tomorrow
