The term "morning person" can be used to describe someone who is not lazy in the morning.
"Not a morning person" refers to the opposite: being lazy in the morning.
There's also the term lark and night owl , referring to people who get up early and go to bed late respectively.
ell.stackexchange.com/users/632/Pubby
Although perhaps not a direct answer to the question, I'd just like to throw in the following phrase that specifically relates to feeling sluggish with perhaps a slight lazy or melancholy connotation, specifically relating to Mondays: Don't talk to Jeff at the moment.
He's got a bad case of the Monday blues With regards to being not being alert and at your best in the mornings, as Pubby suggests
I'm not a morning person which is quite a common expression, meaning someone who isn't at their best in the Mornings - although as Barbara points out, that's not necessarily because of laziness, it might mean someone who just really doesn't enjoy mornings.
There's also a wonderful phrase to describe the opposite, i.e. someone who is always ready to go and enthusiastic in the mornings:
I love how our interns always arrive at work bright eyed and bushy
tailed meaning that the interns are always alert and enthusiastic when they arrive at work.
ell.stackexchange.com/users/307/Matt
The term slugabed denotes “One who indulges in lying late in bed; a sluggard ”.
ell.stackexchange.com/users/146/James Waldby - jwpat7
There's also the phrase "rolling out of bed in the morning" which specifically means that it was difficult to wake up and get out of bed, but is commonly used to describe any type of morning laziness or slow start to a morning.
It's usually used in the past tense such as "I rolled out of the bed this morning" or "I was rolling out of the bed this morning", but can also be used in future tense for situations where someone knows it will be difficult to wake up or get going such as "I'm going to be rolling out of bed tomorrow morning because I need to wake up early to prepare for a presentation".
ell.stackexchange.com/users/15987/Steve
The term Sleep Inertia describes reduced abilities immediately after waking up.
However this is a somewhat technical term that may not be very widely known.
ell.stackexchange.com/users/15746/bdsl
As we all know, some people are lazy when they wake up in the morning.  Is there any term in English expressing  "laziness in mornings" , maybe like  "hangover without alcohol" ?
Is there any term about morning laziness?
ell.stackexchange.com
<phrase-request>
ell.stackexchange.com/questions/2612
ell.stackexchange.com/users/256/Soner Gönül
"Not a morning person"  refers to someone who is lazy in the morning.  Lark  and  night owl , refer to people who get up early and go to bed late, respectively.  "Rolling out of bed in the morning" which specifically describes people who find it difficult to wake up and get out of bed, and the term "slugabed"  denotes  “One who indulges in lying late in bed; a  sluggard ”.  Slugabed, rolling out of bed and sleep inertia are different ways of understanding this. Also, larks and night owls/morning person and not a morning person can be used to distinguish people.
Slugabed, rolling out of bed and sleep inertia are different ways of understanding this. Larks and night owls/morning person and not a morning person can be used to distinguish people.