The verb manquer is often very troublesome for English speakers of French because its structure is reversed when it applies to emotions compared to events.
Look at these sentences with the verb manquer in an emotional sense:
Mon ancienne école me manque .
I miss my old school.
Jean lui manque.
She/he misses Jean
Il manque à ma soeur.
My sister misses him.
Je manque à Thomas.
Thomas misses me.
When using manquer in the emotional sense, you must reverse the structure so it is the person or thing that is lacking to you:
Tu manques à Lise.
Lise misses you.
-> It's not
Lise misses you. anymore, but literally
You are lacking to Lise.
Elle me manque.
I miss her.
-> It's not
I miss her, but literally
She is lacking to me.
Je lui manque.
He misses me.
-> It's not
He misses me, but literally
I am lacking to him.
Now the 'missed' person or thing become the one doing the action of 'lacking'.
Introducing the person who is missing someone, who is "lacking" someone
You either use manquer à + [name]:
Nous manquons à Patricia.
Patricia misses us.
Léo manque à ma sœur.
My sister misses Léo.
or indirect pronouns me/te/lui/nous/vous/leur before manquer :
Hélène leur manque.
They miss Hélène.
Mon chien me manque.
I miss my dog.
It is different when talking about missing an event or a train, or lacking something in a pragmatic way.
See Manquer (de) + thing = To miss / lack something
As for using indirect pronouns, see Me, te, nous, vous = Me, you, us, you (direct and indirect object pronouns) and Replacing people with lui, leur = him, her, them (indirect object pronouns)
Mon chien me manque.
I miss my dog.
Elle me manque.
I miss her.
Tu manques à Lise.
Lise misses you.
Hélène leur manque.
They miss Hélène.
Mon ancienne école me manque .
I miss my old school.
Léo manque à ma sœur.
My sister misses Léo.
Jean lui manque.
She/he misses Jean
Nous manquons à Patricia.
Patricia misses us.
Ma mère me manque.
I miss my mum
Je manque à Thomas.
Thomas misses me.
Je lui manque.
He misses me.
Il manque à ma soeur.
My sister misses him.
