IB from Non target UK?

You honestly have two solid paths in, well done man!

Do you think doing a masters is worth it if I get a offer for audit/corp fin at the big 4? Will a masters from a target help me get into ib? I've seen summer graduate internships in IB for masters students before they start their masters. Will having an offer from LSE help me get one of these?

Masters would be helpful. BUT, a lot of LSE MSc students fail to make it into FO finance, especially without prior relevant experience (Big 4 helps but is not ideal) and in a course that isn't directly related. 

As you're in first year, presumably you're just assuming you'd get an LSE offer? I wouldn't be so sure. It's arguably the only UK university that's harder to get into at the MSc level than at UG; multiple people this year getting into econ PhDs at MIT, Stanford, etc. and getting rejected from LSE MSc courses. From a non-RG university, you're basically going to need to be top 10% of the class to make the application worthwhile. At the PG level, you want to be at LBS, Oxford, Cambridge, Imperial or LSE to make the degree valuable for FO finance (plus Warwick and UCL for STEM related subjects, but less so for econ/finance at MSc level). And no, the LSE MSc decision would come out too late for recruiting; the people who have those internships prior to the MSc have done that off the back of their own personal brand prior to the LSE acceptance. Same with Big 4 too - definitely still an uphill struggle from a non-RG. 

Try to find a real internship this summer, even with a small shop. Or offer to do unpaid research assistant work at a research centre at a "traditional target" - cold email professors and see what you can get. You're making far too many assumptions right now that the LSE and Big 4 options are going to be in play. That will only be the case if you are right at the top of your class, as well as having strong ECs or relevant prior experience. Focus on building those first before worrying about this. 

Yeah, those are great backup plans.

As someone said before the usual alternatives in are:

UG -> LMM Boutique

UG -> Top MiM/MFin 

UG -> Big4/Mid-Tier CF/TAS

UG -> Big4/Mid-Tier Audit -> Big4/Mid-Tier CF/TAS

UG -> 3-6 years professional experience in something -> Top MBA.

Bit late now but there's also the transfer to a target / semi-target route.

For S&T there's also: UG -> Trade Support / Sales Support -> S&T

Ditto AM with: UG -> Portfolio Analyst/Product Analyst -> Investments.

Lots of alternative routes.

Obviously try your best to get into some decent internships in tangential fields that sound interesting. You may end up without a decent job if you focus too much on high finance for now.

How do you assume that you’ll just get the offer for LSEs MSc political economy?

I am likely attending LSEs MSc International Political Economy next year, and while doing my LinkedIn research on the program’s graduates, I noticed that those who landed IB jobs always had amazingly solid internships before their MSc. It would likely be much easier from an MSc Finance.

Then again, my sample size of people I stalked on LinkedIn may not be exhaustive.