Step 1: Identify the recipients.
We must order Bharat Ratna awardees: (K) Sachin Tendulkar, (L) Amartya Sen, (M) Lata Mangeshkar, (N) Nanaji Deshmukh, (O) Atal Bihari Vajpayee.
Step 2: Recall the earliest.
Amartya Sen received the award in 1999, the earliest here, so L is first.
Step 3: Recall the next.
Lata Mangeshkar was honoured in 2001, so M follows L.
Step 4: Recall the 2014 award.
Sachin Tendulkar received it in 2014, so K comes next.
Step 5: Recall the last two.
Atal Bihari Vajpayee was awarded in 2015 and Nanaji Deshmukh posthumously in 2019, so O then N.
Step 6: Assemble the order.
The sequence is $\text{L} \rightarrow \text{M} \rightarrow \text{K} \rightarrow \text{O} \rightarrow \text{N}$, option D.
\[ \boxed{\text{L} \rightarrow \text{M} \rightarrow \text{K} \rightarrow \text{O} \rightarrow \text{N}} \]