Should I invest in this LIC policy?

Avoid. LIC and the agent would take most of it. You'd be left with peanuts. It's one of the most opaque form of investments, and there's no guarantee. Govt. backs LIC, not your financial future.

LIC doesn't create money out of thin air. Over-simplified & shortened description of how it works: It collects premium from policyholders, then it invests that in market-linked securities (bonds, stocks, CP, CD, commodities etc.). Eventually, it pays out policyholders after keeping some cut for itself.
Unlike bank or post-office deposits, LIC returns are not legally guaranteed. Govt. of India is a major stakeholder in LIC, but that does not mean it's a major stakeholder in your future. Govt. would do its best to prevent LIC from going under. But your returns come at the cost of LIC's income - when those two are at odds with each other, Govt. would pick LIC over your financial future.
In practice, LIC returns money you'd paid as premium + some bonus. There are different categories of these bonuses: loyalty bonus, guaranteed addition etc. LIC wants to make you feel they're doing you a favor by giving you some bonus. Historically, a bank FD / RD at SBI would have had higher returns than LIC policy over a given period.
You can know your bonus after the policy matures.
LIC is also not allowed to invest freely. They are the largest financial services company in the country, and have much more cash than any other financial institution, that they can invest. However, large corpus of few lakh crores are not easy to invest. So they have to look for distressed assets, or wait for really bad market condition before deploying sizeable chunk of that cash.
There's also political interference to consider - as evident from LIC's bailout of IDBI bank. LIC's hands are tied, in when it comes to where they can / cannot invest.
Over long enough period of time, LIC returns have also significantly underperformed equity market returns, namely Nifty & Sensex Total Return Index.
Now, consider various charges on insurance (mortality charges, admin fees, risk premium etc.). These are not shown to you (the end policyholders); but these eat away your corpus and line up LIC's pockets.
Your agent would tell you to invest in LIC policy, because that helps him earn commission. Your parents would pressure you into doing it, because most likely they'd not be aware of other investment options.
The fact that it has tax benefits is of little concern, because gains from LIC policies are so low, taxing it won't make much difference in final corpus size, post-tax.
At its core, an LIC policy is an insurance policy. The cover provided by this insurance is inadequate, to take care of your family's financial needs in your absence. A pure term cover is better, which works very different from how a typical LIC policy works.
But none of the above covers real problem with an LIC policy - it locks you into a lifelong decision much early on. For a lot of people, who had subscribed to LIC policies 20-25 years ago, and seeing their policies maturing now - the maturity amount is probably not even worth a month's income.
Due to inflation, the maturity estimate which might look huge today, would be much lower in value, upon actual maturity.
These premiums cannot be changed once you start paying for a policy. You have no option of stepping up your premiums as your salary increases year on year.
Overall, an LIC policy is rigid, wasteful, and doesn't provide adequate coverage. Tax benefits are not good enough to offset the opportunity cost (i.e. you're missing out on other efficient assets and time).
Avoid LIC policies, buy vanilla pure term cover, and invest in efficient market-linked transparent assets yourself. If your question is but what if markets don't do well in next 15-20 years?, then the LIC policy also has same fate.
Addendum
The general perception of the term "LIC policy" is any moneyback/endowment policy, in which there is some investment component also, i.e. after the end of the term of the policy, you will get money returned back to you. There are pure protection plans available by LIC and other insurance companies, which are what are recommended. In case of LIC, these are Jeevan Amar and Jeevan Tech Term. All others are some combination of moneyback plans.

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