OOo err that was a bit of a shock, but at least you do now have an Account and Lloyds did used to have some advantages for Students, such as low interest loan rates to pay back Student borrowings for a couple of years after you leave College or Uni. Mind that is speaking from my experience with lLoyds back in 1982 to 1985 - about 20 years ago!!! So check, don't rely on my 20 yrs old experience!!
However, if you feel that you have done nothing wrong, other than not tick a particular box which may have asked whether you had ever applied to Smile before; And you have personally had no other complications in the interim period; And Smile's Student offering is better than Lloyds, then you can go back to Smile and ask them to reconsider, pointing out that you have had no other complications, if that is in fact the case, simply or merely an oversight in not ticking their box.
The problem these days, Banks have gotten into so much trouble lending or giving Current Accounts to dodgy customers who have defaulted, the Banks just seem to jump a mile if there's any whiff that everything is not on the straight and narrow and upfront.
Still we all learn from our experiences.
Nevertheless Good Luck