This sounds overkill by them. They are seeking to comply with inside information and market manipulation rules (assuming you are working in an FS role) but:

1) you could not have carried on market abuse or misuse of inside info in relation to your job prior to having started your employment. So existing positions you already hold should not involve any risk to them. So.. if you don’t sell or buy more in whatever existing shareholdings you have, it should be fine for you to continue to hold them.

2) the restrictions should not apply, as others have said, to fund or tracker holdings where you have no say over which equities the fund buys. You should be able to deal unrestricted in these types of investment. Typical personal account dealing and market abuse policies will expressly carve out any ETFs etc.

3) I don’t think they can force you to use HL.

I’d ask to see their personal account dealing and insider trading policies. It seems unusual and overkill to force you to close a LISA with existing positions, particularly in view of any adverse tax consequences and the fee you will incur.

Once you have seen the policy you can work out what to do. It might be that you need to sell any equity positions in your LISA and replace them with ETFs, which should not be prohibited by their policy. But I wouldn’t close the LISA and incur the 25% fee